Step |
Hyp |
Ref |
Expression |
1 |
|
hsmexlem4.x |
|
2 |
|
hsmexlem4.h |
|
3 |
|
hsmexlem4.u |
|
4 |
|
hsmexlem4.s |
|
5 |
|
hsmexlem4.o |
|
6 |
4
|
ssrab3 |
|
7 |
6
|
sseli |
|
8 |
|
tcrank |
|
9 |
7 8
|
syl |
|
10 |
3
|
itunitc |
|
11 |
3
|
itunifn |
|
12 |
|
fniunfv |
|
13 |
11 12
|
syl |
|
14 |
10 13
|
eqtr4id |
|
15 |
14
|
imaeq2d |
|
16 |
|
imaiun |
|
17 |
16
|
a1i |
|
18 |
9 15 17
|
3eqtrd |
|
19 |
|
dmresi |
|
20 |
18 19
|
eqtr4di |
|
21 |
|
rankon |
|
22 |
18 21
|
eqeltrrdi |
|
23 |
|
eloni |
|
24 |
|
oiid |
|
25 |
22 23 24
|
3syl |
|
26 |
25
|
dmeqd |
|
27 |
20 26
|
eqtr4d |
|
28 |
|
omex |
|
29 |
|
wdomref |
|
30 |
28 29
|
mp1i |
|
31 |
|
frfnom |
|
32 |
2
|
fneq1i |
|
33 |
31 32
|
mpbir |
|
34 |
|
fniunfv |
|
35 |
33 34
|
ax-mp |
|
36 |
|
iunon |
|
37 |
28 36
|
mpan |
|
38 |
2
|
hsmexlem9 |
|
39 |
37 38
|
mprg |
|
40 |
35 39
|
eqeltrri |
|
41 |
40
|
a1i |
|
42 |
|
fvssunirn |
|
43 |
|
eqid |
|
44 |
1 2 3 4 43
|
hsmexlem4 |
|
45 |
44
|
ancoms |
|
46 |
42 45
|
sseldi |
|
47 |
|
imassrn |
|
48 |
|
rankf |
|
49 |
|
frn |
|
50 |
48 49
|
ax-mp |
|
51 |
47 50
|
sstri |
|
52 |
|
ffun |
|
53 |
|
fvex |
|
54 |
53
|
funimaex |
|
55 |
48 52 54
|
mp2b |
|
56 |
55
|
elpw |
|
57 |
51 56
|
mpbir |
|
58 |
46 57
|
jctil |
|
59 |
58
|
ralrimiva |
|
60 |
|
eqid |
|
61 |
43 60
|
hsmexlem3 |
|
62 |
30 41 59 61
|
syl21anc |
|
63 |
27 62
|
eqeltrd |
|