Step |
Hyp |
Ref |
Expression |
1 |
|
eqtr2 |
|
2 |
|
fvex |
|
3 |
|
fvex |
|
4 |
|
gonafv |
|
5 |
2 3 4
|
mp2an |
|
6 |
|
fvex |
|
7 |
|
fvex |
|
8 |
|
gonafv |
|
9 |
6 7 8
|
mp2an |
|
10 |
5 9
|
eqeq12i |
|
11 |
|
1oex |
|
12 |
|
opex |
|
13 |
11 12
|
opth |
|
14 |
2 3
|
opth |
|
15 |
14
|
anbi2i |
|
16 |
10 13 15
|
3bitri |
|
17 |
|
funfv1st2nd |
|
18 |
17
|
ex |
|
19 |
|
funfv1st2nd |
|
20 |
19
|
ex |
|
21 |
18 20
|
anim12d |
|
22 |
|
funfv1st2nd |
|
23 |
22
|
ex |
|
24 |
|
funfv1st2nd |
|
25 |
24
|
ex |
|
26 |
23 25
|
anim12d |
|
27 |
|
fveq2 |
|
28 |
27
|
eqcoms |
|
29 |
28
|
adantr |
|
30 |
29
|
eqeq1d |
|
31 |
|
fveq2 |
|
32 |
31
|
eqcoms |
|
33 |
32
|
adantl |
|
34 |
33
|
eqeq1d |
|
35 |
30 34
|
anbi12d |
|
36 |
35
|
anbi1d |
|
37 |
|
eqtr2 |
|
38 |
37
|
ad2ant2r |
|
39 |
|
eqtr2 |
|
40 |
39
|
ad2ant2l |
|
41 |
38 40
|
ineq12d |
|
42 |
36 41
|
syl6bi |
|
43 |
42
|
com12 |
|
44 |
43
|
a1i |
|
45 |
21 26 44
|
syl2and |
|
46 |
45
|
expd |
|
47 |
46
|
3imp1 |
|
48 |
47
|
difeq2d |
|
49 |
48
|
adantr |
|
50 |
|
eqeq12 |
|
51 |
50
|
adantl |
|
52 |
49 51
|
mpbird |
|
53 |
52
|
exp43 |
|
54 |
53
|
adantld |
|
55 |
16 54
|
syl5bi |
|
56 |
1 55
|
syl5 |
|
57 |
56
|
expd |
|
58 |
57
|
com35 |
|
59 |
58
|
impd |
|
60 |
59
|
com24 |
|
61 |
60
|
impd |
|
62 |
61
|
3imp |
|