Step |
Hyp |
Ref |
Expression |
1 |
|
2arymaptf.h |
Could not format H = ( h e. ( 2 -aryF X ) |-> ( x e. X , y e. X |-> ( h ` { <. 0 , x >. , <. 1 , y >. } ) ) ) : No typesetting found for |- H = ( h e. ( 2 -aryF X ) |-> ( x e. X , y e. X |-> ( h ` { <. 0 , x >. , <. 1 , y >. } ) ) ) with typecode |- |
2 |
1
|
2arymaptf |
Could not format ( X e. V -> H : ( 2 -aryF X ) --> ( X ^m ( X X. X ) ) ) : No typesetting found for |- ( X e. V -> H : ( 2 -aryF X ) --> ( X ^m ( X X. X ) ) ) with typecode |- |
3 |
1
|
2arymaptfv |
Could not format ( f e. ( 2 -aryF X ) -> ( H ` f ) = ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) ) : No typesetting found for |- ( f e. ( 2 -aryF X ) -> ( H ` f ) = ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) ) with typecode |- |
4 |
3
|
ad2antrl |
Could not format ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( H ` f ) = ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) ) : No typesetting found for |- ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( H ` f ) = ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) ) with typecode |- |
5 |
1
|
2arymaptfv |
Could not format ( g e. ( 2 -aryF X ) -> ( H ` g ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) ) : No typesetting found for |- ( g e. ( 2 -aryF X ) -> ( H ` g ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) ) with typecode |- |
6 |
5
|
ad2antll |
Could not format ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( H ` g ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) ) : No typesetting found for |- ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( H ` g ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) ) with typecode |- |
7 |
4 6
|
eqeq12d |
Could not format ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( ( H ` f ) = ( H ` g ) <-> ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) ) ) : No typesetting found for |- ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( ( H ` f ) = ( H ` g ) <-> ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) ) ) with typecode |- |
8 |
|
fvex |
|
9 |
8
|
rgen2w |
|
10 |
|
mpo2eqb |
|
11 |
9 10
|
mp1i |
Could not format ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) <-> A. x e. X A. y e. X ( f ` { <. 0 , x >. , <. 1 , y >. } ) = ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) ) : No typesetting found for |- ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) <-> A. x e. X A. y e. X ( f ` { <. 0 , x >. , <. 1 , y >. } ) = ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) ) with typecode |- |
12 |
|
2aryfvalel |
Could not format ( X e. V -> ( f e. ( 2 -aryF X ) <-> f : ( X ^m { 0 , 1 } ) --> X ) ) : No typesetting found for |- ( X e. V -> ( f e. ( 2 -aryF X ) <-> f : ( X ^m { 0 , 1 } ) --> X ) ) with typecode |- |
13 |
|
2aryfvalel |
Could not format ( X e. V -> ( g e. ( 2 -aryF X ) <-> g : ( X ^m { 0 , 1 } ) --> X ) ) : No typesetting found for |- ( X e. V -> ( g e. ( 2 -aryF X ) <-> g : ( X ^m { 0 , 1 } ) --> X ) ) with typecode |- |
14 |
12 13
|
anbi12d |
Could not format ( X e. V -> ( ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) <-> ( f : ( X ^m { 0 , 1 } ) --> X /\ g : ( X ^m { 0 , 1 } ) --> X ) ) ) : No typesetting found for |- ( X e. V -> ( ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) <-> ( f : ( X ^m { 0 , 1 } ) --> X /\ g : ( X ^m { 0 , 1 } ) --> X ) ) ) with typecode |- |
15 |
|
ffn |
|
16 |
15
|
adantr |
|
17 |
16
|
3ad2ant2 |
|
18 |
|
ffn |
|
19 |
18
|
adantl |
|
20 |
19
|
3ad2ant2 |
|
21 |
|
elmapi |
|
22 |
|
0ne1 |
|
23 |
|
c0ex |
|
24 |
|
1ex |
|
25 |
23 24
|
fprb |
|
26 |
22 25
|
ax-mp |
|
27 |
21 26
|
sylib |
|
28 |
|
opeq2 |
|
29 |
28
|
preq1d |
|
30 |
29
|
fveq2d |
|
31 |
29
|
fveq2d |
|
32 |
30 31
|
eqeq12d |
|
33 |
|
opeq2 |
|
34 |
33
|
preq2d |
|
35 |
34
|
fveq2d |
|
36 |
34
|
fveq2d |
|
37 |
35 36
|
eqeq12d |
|
38 |
32 37
|
rspc2va |
|
39 |
38
|
expcom |
|
40 |
39
|
3ad2ant3 |
|
41 |
40
|
com12 |
|
42 |
41
|
adantr |
|
43 |
|
fveq2 |
|
44 |
|
fveq2 |
|
45 |
43 44
|
eqeq12d |
|
46 |
45
|
adantl |
|
47 |
42 46
|
sylibrd |
|
48 |
47
|
ex |
|
49 |
48
|
rexlimivv |
|
50 |
27 49
|
syl |
|
51 |
50
|
impcom |
|
52 |
17 20 51
|
eqfnfvd |
|
53 |
52
|
3exp |
|
54 |
14 53
|
sylbid |
Could not format ( X e. V -> ( ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) -> ( A. x e. X A. y e. X ( f ` { <. 0 , x >. , <. 1 , y >. } ) = ( g ` { <. 0 , x >. , <. 1 , y >. } ) -> f = g ) ) ) : No typesetting found for |- ( X e. V -> ( ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) -> ( A. x e. X A. y e. X ( f ` { <. 0 , x >. , <. 1 , y >. } ) = ( g ` { <. 0 , x >. , <. 1 , y >. } ) -> f = g ) ) ) with typecode |- |
55 |
54
|
imp |
Could not format ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( A. x e. X A. y e. X ( f ` { <. 0 , x >. , <. 1 , y >. } ) = ( g ` { <. 0 , x >. , <. 1 , y >. } ) -> f = g ) ) : No typesetting found for |- ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( A. x e. X A. y e. X ( f ` { <. 0 , x >. , <. 1 , y >. } ) = ( g ` { <. 0 , x >. , <. 1 , y >. } ) -> f = g ) ) with typecode |- |
56 |
11 55
|
sylbid |
Could not format ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) -> f = g ) ) : No typesetting found for |- ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( ( x e. X , y e. X |-> ( f ` { <. 0 , x >. , <. 1 , y >. } ) ) = ( x e. X , y e. X |-> ( g ` { <. 0 , x >. , <. 1 , y >. } ) ) -> f = g ) ) with typecode |- |
57 |
7 56
|
sylbid |
Could not format ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( ( H ` f ) = ( H ` g ) -> f = g ) ) : No typesetting found for |- ( ( X e. V /\ ( f e. ( 2 -aryF X ) /\ g e. ( 2 -aryF X ) ) ) -> ( ( H ` f ) = ( H ` g ) -> f = g ) ) with typecode |- |
58 |
57
|
ralrimivva |
Could not format ( X e. V -> A. f e. ( 2 -aryF X ) A. g e. ( 2 -aryF X ) ( ( H ` f ) = ( H ` g ) -> f = g ) ) : No typesetting found for |- ( X e. V -> A. f e. ( 2 -aryF X ) A. g e. ( 2 -aryF X ) ( ( H ` f ) = ( H ` g ) -> f = g ) ) with typecode |- |
59 |
|
dff13 |
Could not format ( H : ( 2 -aryF X ) -1-1-> ( X ^m ( X X. X ) ) <-> ( H : ( 2 -aryF X ) --> ( X ^m ( X X. X ) ) /\ A. f e. ( 2 -aryF X ) A. g e. ( 2 -aryF X ) ( ( H ` f ) = ( H ` g ) -> f = g ) ) ) : No typesetting found for |- ( H : ( 2 -aryF X ) -1-1-> ( X ^m ( X X. X ) ) <-> ( H : ( 2 -aryF X ) --> ( X ^m ( X X. X ) ) /\ A. f e. ( 2 -aryF X ) A. g e. ( 2 -aryF X ) ( ( H ` f ) = ( H ` g ) -> f = g ) ) ) with typecode |- |
60 |
2 58 59
|
sylanbrc |
Could not format ( X e. V -> H : ( 2 -aryF X ) -1-1-> ( X ^m ( X X. X ) ) ) : No typesetting found for |- ( X e. V -> H : ( 2 -aryF X ) -1-1-> ( X ^m ( X X. X ) ) ) with typecode |- |