Step |
Hyp |
Ref |
Expression |
1 |
|
satfv1fvfmla1.x |
|
2 |
1
|
ovexi |
|
3 |
2
|
jctr |
|
4 |
3
|
3ad2ant1 |
|
5 |
|
satefv |
|
6 |
4 5
|
syl |
|
7 |
|
sqxpexg |
|
8 |
|
inex2g |
|
9 |
7 8
|
syl |
|
10 |
9
|
ancli |
|
11 |
10
|
3ad2ant1 |
|
12 |
|
satom |
|
13 |
11 12
|
syl |
|
14 |
13
|
fveq1d |
|
15 |
|
satfun |
|
16 |
11 15
|
syl |
|
17 |
16
|
ffund |
|
18 |
13
|
eqcomd |
|
19 |
18
|
funeqd |
|
20 |
17 19
|
mpbird |
|
21 |
|
1onn |
|
22 |
21
|
a1i |
|
23 |
1
|
2goelgoanfmla1 |
|
24 |
23
|
3adant1 |
|
25 |
21
|
a1i |
|
26 |
|
satfdmfmla |
|
27 |
9 25 26
|
mpd3an23 |
|
28 |
27
|
3ad2ant1 |
|
29 |
24 28
|
eleqtrrd |
|
30 |
|
eqid |
|
31 |
30
|
fviunfun |
|
32 |
20 22 29 31
|
syl3anc |
|
33 |
14 32
|
eqtrd |
|
34 |
1
|
satfv1fvfmla1 |
|
35 |
10 34
|
syl3an1 |
|
36 |
|
brin |
|
37 |
|
elmapi |
|
38 |
|
ffvelrn |
|
39 |
38
|
ex |
|
40 |
37 39
|
syl |
|
41 |
|
ffvelrn |
|
42 |
41
|
ex |
|
43 |
37 42
|
syl |
|
44 |
40 43
|
anim12d |
|
45 |
44
|
com12 |
|
46 |
45
|
3ad2ant2 |
|
47 |
46
|
imp |
|
48 |
|
brxp |
|
49 |
47 48
|
sylibr |
|
50 |
49
|
biantrud |
|
51 |
|
fvex |
|
52 |
51
|
epeli |
|
53 |
50 52
|
bitr3di |
|
54 |
36 53
|
syl5bb |
|
55 |
54
|
notbid |
|
56 |
|
brin |
|
57 |
|
ffvelrn |
|
58 |
57
|
ex |
|
59 |
37 58
|
syl |
|
60 |
|
ffvelrn |
|
61 |
60
|
ex |
|
62 |
37 61
|
syl |
|
63 |
59 62
|
anim12d |
|
64 |
63
|
com12 |
|
65 |
64
|
3ad2ant3 |
|
66 |
65
|
imp |
|
67 |
|
brxp |
|
68 |
66 67
|
sylibr |
|
69 |
68
|
biantrud |
|
70 |
|
fvex |
|
71 |
70
|
epeli |
|
72 |
69 71
|
bitr3di |
|
73 |
56 72
|
syl5bb |
|
74 |
73
|
notbid |
|
75 |
55 74
|
orbi12d |
|
76 |
75
|
rabbidva |
|
77 |
35 76
|
eqtrd |
|
78 |
6 33 77
|
3eqtrd |
|