Step |
Hyp |
Ref |
Expression |
1 |
|
f1prex.1 |
|
2 |
|
f1prex.2 |
|
3 |
|
simpl1 |
|
4 |
|
simpl2 |
|
5 |
|
simprl |
|
6 |
|
f1f |
|
7 |
5 6
|
syl |
|
8 |
|
fpr2g |
|
9 |
8
|
biimpa |
|
10 |
9
|
simp1d |
|
11 |
3 4 7 10
|
syl21anc |
|
12 |
9
|
simp2d |
|
13 |
3 4 7 12
|
syl21anc |
|
14 |
|
prid1g |
|
15 |
3 14
|
syl |
|
16 |
|
prid2g |
|
17 |
4 16
|
syl |
|
18 |
15 17
|
jca |
|
19 |
|
simpl3 |
|
20 |
|
f1veqaeq |
|
21 |
20
|
necon3d |
|
22 |
21
|
imp |
|
23 |
5 18 19 22
|
syl21anc |
|
24 |
|
simprr |
|
25 |
23 24
|
jca |
|
26 |
|
neeq1 |
|
27 |
26 1
|
anbi12d |
|
28 |
|
neeq2 |
|
29 |
28 2
|
anbi12d |
|
30 |
27 29
|
rspc2ev |
|
31 |
11 13 25 30
|
syl3anc |
|
32 |
31
|
ex |
|
33 |
32
|
exlimdv |
|
34 |
|
simpll1 |
|
35 |
|
simplrl |
|
36 |
34 35
|
jca |
|
37 |
|
simpll2 |
|
38 |
|
simplrr |
|
39 |
37 38
|
jca |
|
40 |
|
simpll3 |
|
41 |
|
simprl |
|
42 |
|
f1oprg |
|
43 |
42
|
imp |
|
44 |
36 39 40 41 43
|
syl22anc |
|
45 |
|
f1of1 |
|
46 |
44 45
|
syl |
|
47 |
35 38
|
prssd |
|
48 |
|
f1ss |
|
49 |
46 47 48
|
syl2anc |
|
50 |
|
fvpr1g |
|
51 |
50
|
eqcomd |
|
52 |
34 35 40 51
|
syl3anc |
|
53 |
|
fvpr2g |
|
54 |
53
|
eqcomd |
|
55 |
37 38 40 54
|
syl3anc |
|
56 |
|
prex |
|
57 |
|
f1eq1 |
|
58 |
|
fveq1 |
|
59 |
58
|
eqeq2d |
|
60 |
|
fveq1 |
|
61 |
60
|
eqeq2d |
|
62 |
59 61
|
anbi12d |
|
63 |
57 62
|
anbi12d |
|
64 |
56 63
|
spcev |
|
65 |
49 52 55 64
|
syl12anc |
|
66 |
|
simprl |
|
67 |
|
simplrr |
|
68 |
|
simprrl |
|
69 |
68 1
|
syl |
|
70 |
67 69
|
mpbid |
|
71 |
|
simprrr |
|
72 |
71 2
|
syl |
|
73 |
70 72
|
mpbid |
|
74 |
66 73
|
jca |
|
75 |
74
|
ex |
|
76 |
75
|
eximdv |
|
77 |
65 76
|
mpd |
|
78 |
77
|
ex |
|
79 |
78
|
rexlimdvva |
|
80 |
33 79
|
impbid |
|