Step |
Hyp |
Ref |
Expression |
1 |
|
eqeq1 |
|
2 |
|
eqeq1 |
|
3 |
1 2
|
orbi12d |
|
4 |
3
|
reu8 |
|
5 |
|
simprlr |
|
6 |
|
eqeq1 |
|
7 |
|
eqeq1 |
|
8 |
6 7
|
orbi12d |
|
9 |
|
eqeq2 |
|
10 |
8 9
|
imbi12d |
|
11 |
10
|
rspcv |
|
12 |
5 11
|
syl |
|
13 |
|
ioran |
|
14 |
|
eqid |
|
15 |
14
|
pm2.24i |
|
16 |
13 15
|
simplbiim |
|
17 |
|
eqtr2 |
|
18 |
17
|
ancoms |
|
19 |
18
|
a1d |
|
20 |
19
|
expimpd |
|
21 |
16 20
|
ja |
|
22 |
21
|
com12 |
|
23 |
12 22
|
syld |
|
24 |
23
|
ex |
|
25 |
|
simprll |
|
26 |
|
eqeq1 |
|
27 |
|
eqeq1 |
|
28 |
26 27
|
orbi12d |
|
29 |
|
eqeq2 |
|
30 |
28 29
|
imbi12d |
|
31 |
30
|
rspcv |
|
32 |
25 31
|
syl |
|
33 |
|
ioran |
|
34 |
|
eqid |
|
35 |
34
|
pm2.24i |
|
36 |
35
|
adantr |
|
37 |
33 36
|
sylbi |
|
38 |
17
|
a1d |
|
39 |
38
|
expimpd |
|
40 |
37 39
|
ja |
|
41 |
40
|
com12 |
|
42 |
32 41
|
syld |
|
43 |
42
|
ex |
|
44 |
24 43
|
jaoi |
|
45 |
44
|
com12 |
|
46 |
45
|
impd |
|
47 |
46
|
rexlimdva |
|
48 |
4 47
|
syl5bi |
|
49 |
|
reueq |
|
50 |
49
|
biimpi |
|
51 |
50
|
adantl |
|
52 |
51
|
adantr |
|
53 |
|
eqeq2 |
|
54 |
53
|
adantl |
|
55 |
54
|
orbi1d |
|
56 |
|
oridm |
|
57 |
55 56
|
syl6bb |
|
58 |
57
|
reubidv |
|
59 |
52 58
|
mpbird |
|
60 |
59
|
ex |
|
61 |
48 60
|
impbid |
|