Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
|
eqid |
|
5 |
1 2 3 4
|
isomgr |
|
6 |
5
|
3adant3 |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
2 7 4 8
|
isomgr |
|
10 |
9
|
3adant1 |
|
11 |
6 10
|
anbi12d |
|
12 |
|
vex |
|
13 |
|
vex |
|
14 |
12 13
|
coex |
|
15 |
14
|
a1i |
|
16 |
|
simpl |
|
17 |
|
simprl |
|
18 |
|
f1oco |
|
19 |
16 17 18
|
syl2anr |
|
20 |
|
vex |
|
21 |
|
vex |
|
22 |
20 21
|
coex |
|
23 |
22
|
a1i |
|
24 |
|
simpl |
|
25 |
|
simprl |
|
26 |
|
f1oco |
|
27 |
24 25 26
|
syl2anr |
|
28 |
|
isomgrtrlem |
|
29 |
27 28
|
jca |
|
30 |
|
f1oeq1 |
|
31 |
|
fveq1 |
|
32 |
31
|
fveq2d |
|
33 |
32
|
eqeq2d |
|
34 |
33
|
ralbidv |
|
35 |
30 34
|
anbi12d |
|
36 |
23 29 35
|
spcedv |
|
37 |
36
|
ex |
|
38 |
37
|
exlimdv |
|
39 |
38
|
ex |
|
40 |
39
|
exlimdv |
|
41 |
40
|
3exp |
|
42 |
41
|
com34 |
|
43 |
42
|
imp32 |
|
44 |
43
|
imp32 |
|
45 |
19 44
|
jca |
|
46 |
|
f1oeq1 |
|
47 |
|
imaeq1 |
|
48 |
47
|
eqeq1d |
|
49 |
48
|
ralbidv |
|
50 |
49
|
anbi2d |
|
51 |
50
|
exbidv |
|
52 |
46 51
|
anbi12d |
|
53 |
15 45 52
|
spcedv |
|
54 |
1 7 3 8
|
isomgr |
|
55 |
54
|
3adant2 |
|
56 |
55
|
ad2antrr |
|
57 |
53 56
|
mpbird |
|
58 |
57
|
ex |
|
59 |
58
|
exlimdv |
|
60 |
59
|
ex |
|
61 |
60
|
exlimdv |
|
62 |
61
|
impd |
|
63 |
11 62
|
sylbid |
|