Step |
Hyp |
Ref |
Expression |
1 |
|
2fveq3 |
Could not format ( x = xO -> ( bday ` ( -us ` x ) ) = ( bday ` ( -us ` xO ) ) ) : No typesetting found for |- ( x = xO -> ( bday ` ( -us ` x ) ) = ( bday ` ( -us ` xO ) ) ) with typecode |- |
2 |
|
fveq2 |
Could not format ( x = xO -> ( bday ` x ) = ( bday ` xO ) ) : No typesetting found for |- ( x = xO -> ( bday ` x ) = ( bday ` xO ) ) with typecode |- |
3 |
1 2
|
sseq12d |
Could not format ( x = xO -> ( ( bday ` ( -us ` x ) ) C_ ( bday ` x ) <-> ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) ) : No typesetting found for |- ( x = xO -> ( ( bday ` ( -us ` x ) ) C_ ( bday ` x ) <-> ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) ) with typecode |- |
4 |
|
2fveq3 |
|
5 |
|
fveq2 |
|
6 |
4 5
|
sseq12d |
|
7 |
|
negsval |
|
8 |
7
|
fveq2d |
|
9 |
8
|
adantr |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday ` ( -us ` x ) ) = ( bday ` ( ( -us " ( _Right ` x ) ) |s ( -us " ( _Left ` x ) ) ) ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday ` ( -us ` x ) ) = ( bday ` ( ( -us " ( _Right ` x ) ) |s ( -us " ( _Left ` x ) ) ) ) ) with typecode |- |
10 |
|
negscut2 |
|
11 |
|
lrold |
|
12 |
|
uncom |
|
13 |
11 12
|
eqtr3i |
|
14 |
13
|
imaeq2i |
|
15 |
|
imaundi |
|
16 |
14 15
|
eqtri |
|
17 |
16
|
imaeq2i |
|
18 |
11
|
raleqi |
Could not format ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) <-> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) : No typesetting found for |- ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) <-> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) with typecode |- |
19 |
|
oldbdayim |
Could not format ( xO e. ( _Old ` ( bday ` x ) ) -> ( bday ` xO ) e. ( bday ` x ) ) : No typesetting found for |- ( xO e. ( _Old ` ( bday ` x ) ) -> ( bday ` xO ) e. ( bday ` x ) ) with typecode |- |
20 |
19
|
adantl |
Could not format ( ( x e. No /\ xO e. ( _Old ` ( bday ` x ) ) ) -> ( bday ` xO ) e. ( bday ` x ) ) : No typesetting found for |- ( ( x e. No /\ xO e. ( _Old ` ( bday ` x ) ) ) -> ( bday ` xO ) e. ( bday ` x ) ) with typecode |- |
21 |
|
bdayelon |
Could not format ( bday ` ( -us ` xO ) ) e. On : No typesetting found for |- ( bday ` ( -us ` xO ) ) e. On with typecode |- |
22 |
|
bdayelon |
|
23 |
|
ontr2 |
Could not format ( ( ( bday ` ( -us ` xO ) ) e. On /\ ( bday ` x ) e. On ) -> ( ( ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) /\ ( bday ` xO ) e. ( bday ` x ) ) -> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) : No typesetting found for |- ( ( ( bday ` ( -us ` xO ) ) e. On /\ ( bday ` x ) e. On ) -> ( ( ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) /\ ( bday ` xO ) e. ( bday ` x ) ) -> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) with typecode |- |
24 |
21 22 23
|
mp2an |
Could not format ( ( ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) /\ ( bday ` xO ) e. ( bday ` x ) ) -> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) : No typesetting found for |- ( ( ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) /\ ( bday ` xO ) e. ( bday ` x ) ) -> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) with typecode |- |
25 |
24
|
a1i |
Could not format ( ( x e. No /\ xO e. ( _Old ` ( bday ` x ) ) ) -> ( ( ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) /\ ( bday ` xO ) e. ( bday ` x ) ) -> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) : No typesetting found for |- ( ( x e. No /\ xO e. ( _Old ` ( bday ` x ) ) ) -> ( ( ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) /\ ( bday ` xO ) e. ( bday ` x ) ) -> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) with typecode |- |
26 |
20 25
|
mpan2d |
Could not format ( ( x e. No /\ xO e. ( _Old ` ( bday ` x ) ) ) -> ( ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) -> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) : No typesetting found for |- ( ( x e. No /\ xO e. ( _Old ` ( bday ` x ) ) ) -> ( ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) -> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) with typecode |- |
27 |
26
|
ralimdva |
Could not format ( x e. No -> ( A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) -> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) : No typesetting found for |- ( x e. No -> ( A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) -> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) with typecode |- |
28 |
27
|
imp |
Could not format ( ( x e. No /\ A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) with typecode |- |
29 |
|
bdayfun |
|
30 |
|
imassrn |
|
31 |
|
bdaydm |
|
32 |
|
negsfo |
|
33 |
|
forn |
|
34 |
32 33
|
ax-mp |
|
35 |
31 34
|
eqtr4i |
|
36 |
30 35
|
sseqtrri |
|
37 |
|
funimass4 |
|
38 |
29 36 37
|
mp2an |
|
39 |
|
negsfn |
|
40 |
|
oldssno |
|
41 |
|
fveq2 |
Could not format ( y = ( -us ` xO ) -> ( bday ` y ) = ( bday ` ( -us ` xO ) ) ) : No typesetting found for |- ( y = ( -us ` xO ) -> ( bday ` y ) = ( bday ` ( -us ` xO ) ) ) with typecode |- |
42 |
41
|
eleq1d |
Could not format ( y = ( -us ` xO ) -> ( ( bday ` y ) e. ( bday ` x ) <-> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) : No typesetting found for |- ( y = ( -us ` xO ) -> ( ( bday ` y ) e. ( bday ` x ) <-> ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) with typecode |- |
43 |
42
|
imaeqsalv |
Could not format ( ( -us Fn No /\ ( _Old ` ( bday ` x ) ) C_ No ) -> ( A. y e. ( -us " ( _Old ` ( bday ` x ) ) ) ( bday ` y ) e. ( bday ` x ) <-> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) : No typesetting found for |- ( ( -us Fn No /\ ( _Old ` ( bday ` x ) ) C_ No ) -> ( A. y e. ( -us " ( _Old ` ( bday ` x ) ) ) ( bday ` y ) e. ( bday ` x ) <-> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) ) with typecode |- |
44 |
39 40 43
|
mp2an |
Could not format ( A. y e. ( -us " ( _Old ` ( bday ` x ) ) ) ( bday ` y ) e. ( bday ` x ) <-> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) : No typesetting found for |- ( A. y e. ( -us " ( _Old ` ( bday ` x ) ) ) ( bday ` y ) e. ( bday ` x ) <-> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) with typecode |- |
45 |
38 44
|
bitri |
Could not format ( ( bday " ( -us " ( _Old ` ( bday ` x ) ) ) ) C_ ( bday ` x ) <-> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) : No typesetting found for |- ( ( bday " ( -us " ( _Old ` ( bday ` x ) ) ) ) C_ ( bday ` x ) <-> A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) e. ( bday ` x ) ) with typecode |- |
46 |
28 45
|
sylibr |
Could not format ( ( x e. No /\ A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday " ( -us " ( _Old ` ( bday ` x ) ) ) ) C_ ( bday ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( _Old ` ( bday ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday " ( -us " ( _Old ` ( bday ` x ) ) ) ) C_ ( bday ` x ) ) with typecode |- |
47 |
18 46
|
sylan2b |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday " ( -us " ( _Old ` ( bday ` x ) ) ) ) C_ ( bday ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday " ( -us " ( _Old ` ( bday ` x ) ) ) ) C_ ( bday ` x ) ) with typecode |- |
48 |
17 47
|
eqsstrrid |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday " ( ( -us " ( _Right ` x ) ) u. ( -us " ( _Left ` x ) ) ) ) C_ ( bday ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday " ( ( -us " ( _Right ` x ) ) u. ( -us " ( _Left ` x ) ) ) ) C_ ( bday ` x ) ) with typecode |- |
49 |
|
scutbdaybnd |
|
50 |
22 49
|
mp3an2 |
|
51 |
10 48 50
|
syl2an2r |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday ` ( ( -us " ( _Right ` x ) ) |s ( -us " ( _Left ` x ) ) ) ) C_ ( bday ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday ` ( ( -us " ( _Right ` x ) ) |s ( -us " ( _Left ` x ) ) ) ) C_ ( bday ` x ) ) with typecode |- |
52 |
9 51
|
eqsstrd |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday ` ( -us ` x ) ) C_ ( bday ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) ) -> ( bday ` ( -us ` x ) ) C_ ( bday ` x ) ) with typecode |- |
53 |
52
|
ex |
Could not format ( x e. No -> ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) -> ( bday ` ( -us ` x ) ) C_ ( bday ` x ) ) ) : No typesetting found for |- ( x e. No -> ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( bday ` ( -us ` xO ) ) C_ ( bday ` xO ) -> ( bday ` ( -us ` x ) ) C_ ( bday ` x ) ) ) with typecode |- |
54 |
3 6 53
|
noinds |
|