Step |
Hyp |
Ref |
Expression |
1 |
|
gaid.1 |
|
2 |
|
elex |
|
3 |
2
|
anim2i |
|
4 |
|
eqid |
|
5 |
1 4
|
grpidcl |
|
6 |
5
|
adantr |
|
7 |
|
ovres |
|
8 |
|
df-ov |
|
9 |
|
fvex |
|
10 |
|
vex |
|
11 |
9 10
|
op2nd |
|
12 |
8 11
|
eqtri |
|
13 |
7 12
|
eqtrdi |
|
14 |
6 13
|
sylan |
|
15 |
|
simprl |
|
16 |
|
simplr |
|
17 |
|
ovres |
|
18 |
|
df-ov |
|
19 |
|
vex |
|
20 |
19 10
|
op2nd |
|
21 |
18 20
|
eqtri |
|
22 |
17 21
|
eqtrdi |
|
23 |
15 16 22
|
syl2anc |
|
24 |
|
simprr |
|
25 |
|
ovres |
|
26 |
|
df-ov |
|
27 |
|
vex |
|
28 |
27 10
|
op2nd |
|
29 |
26 28
|
eqtri |
|
30 |
25 29
|
eqtrdi |
|
31 |
24 16 30
|
syl2anc |
|
32 |
31
|
oveq2d |
|
33 |
|
eqid |
|
34 |
1 33
|
grpcl |
|
35 |
34
|
3expb |
|
36 |
35
|
ad4ant14 |
|
37 |
|
ovres |
|
38 |
|
df-ov |
|
39 |
|
ovex |
|
40 |
39 10
|
op2nd |
|
41 |
38 40
|
eqtri |
|
42 |
37 41
|
eqtrdi |
|
43 |
36 16 42
|
syl2anc |
|
44 |
23 32 43
|
3eqtr4rd |
|
45 |
44
|
ralrimivva |
|
46 |
14 45
|
jca |
|
47 |
46
|
ralrimiva |
|
48 |
|
f2ndres |
|
49 |
47 48
|
jctil |
|
50 |
1 33 4
|
isga |
|
51 |
3 49 50
|
sylanbrc |
|