Step |
Hyp |
Ref |
Expression |
1 |
|
fmla0 |
|
2 |
|
rabab |
|
3 |
|
abeq1 |
|
4 |
|
goel |
|
5 |
4
|
eqeq2d |
|
6 |
5
|
2rexbiia |
|
7 |
|
0ex |
|
8 |
7
|
snid |
|
9 |
8
|
a1i |
|
10 |
|
opelxpi |
|
11 |
9 10
|
opelxpd |
|
12 |
|
eleq1 |
|
13 |
11 12
|
syl5ibrcom |
|
14 |
13
|
rexlimivv |
|
15 |
|
elxpi |
|
16 |
|
elsni |
|
17 |
16
|
opeq1d |
|
18 |
17
|
eqeq2d |
|
19 |
18
|
adantr |
|
20 |
|
elxpi |
|
21 |
|
simprr |
|
22 |
|
simpl |
|
23 |
|
opeq2 |
|
24 |
23
|
adantr |
|
25 |
24
|
adantl |
|
26 |
22 25
|
eqtrd |
|
27 |
21 26
|
jca |
|
28 |
27
|
ex |
|
29 |
28
|
2eximdv |
|
30 |
|
r2ex |
|
31 |
29 30
|
syl6ibr |
|
32 |
20 31
|
syl5com |
|
33 |
32
|
adantl |
|
34 |
19 33
|
sylbid |
|
35 |
34
|
impcom |
|
36 |
35
|
exlimivv |
|
37 |
15 36
|
syl |
|
38 |
14 37
|
impbii |
|
39 |
6 38
|
bitri |
|
40 |
3 39
|
mpgbir |
|
41 |
1 2 40
|
3eqtri |
|