Step |
Hyp |
Ref |
Expression |
1 |
|
eleq1 |
|
2 |
1
|
biimpac |
|
3 |
|
rabid |
|
4 |
3
|
simplbi2com |
|
5 |
2 4
|
syl |
|
6 |
5
|
impancom |
|
7 |
6
|
ancrd |
|
8 |
7
|
expimpd |
|
9 |
8
|
reximdv2 |
|
10 |
9
|
ralimia |
|
11 |
3
|
simplbi |
|
12 |
6
|
pm4.71rd |
|
13 |
|
df-mpt |
|
14 |
13
|
breqi |
|
15 |
|
df-br |
|
16 |
|
opabidw |
|
17 |
14 15 16
|
3bitri |
|
18 |
12 17
|
bitr4di |
|
19 |
11 18
|
sylan2 |
|
20 |
19
|
rexbidva |
|
21 |
20
|
ralbiia |
|
22 |
|
breq2 |
|
23 |
22
|
rexbidv |
|
24 |
|
nfcv |
|
25 |
|
nfrab1 |
|
26 |
|
nfcv |
|
27 |
|
nfmpt1 |
|
28 |
|
nfcv |
|
29 |
26 27 28
|
nfbr |
|
30 |
|
nfv |
|
31 |
|
breq1 |
|
32 |
24 25 29 30 31
|
cbvrexfw |
|
33 |
23 32
|
syl6bb |
|
34 |
33
|
cbvralvw |
|
35 |
21 34
|
bitr4i |
|
36 |
10 35
|
sylib |
|
37 |
|
nfv |
|
38 |
25
|
nfcri |
|
39 |
|
nfcsb1v |
|
40 |
39
|
nfeq2 |
|
41 |
38 40
|
nfan |
|
42 |
|
eleq1 |
|
43 |
|
csbeq1a |
|
44 |
43
|
eqeq2d |
|
45 |
42 44
|
anbi12d |
|
46 |
37 41 45
|
cbvopab1 |
|
47 |
|
df-mpt |
|
48 |
46 13 47
|
3eqtr4i |
|
49 |
|
nfcv |
|
50 |
39
|
nfel1 |
|
51 |
43
|
eleq1d |
|
52 |
26 49 50 51
|
elrabf |
|
53 |
52
|
simprbi |
|
54 |
48 53
|
fmpti |
|
55 |
36 54
|
jctil |
|
56 |
|
dffo4 |
|
57 |
55 56
|
sylibr |
|
58 |
57
|
adantl |
|
59 |
|
relen |
|
60 |
59
|
brrelex2i |
|
61 |
|
ssrab2 |
|
62 |
|
ssdomg |
|
63 |
60 61 62
|
mpisyl |
|
64 |
|
ensym |
|
65 |
|
domentr |
|
66 |
63 64 65
|
syl2anc |
|
67 |
66
|
ad2antlr |
|
68 |
|
enfi |
|
69 |
68
|
biimpac |
|
70 |
|
rabfi |
|
71 |
69 70
|
syl |
|
72 |
|
fodomfi |
|
73 |
71 57 72
|
syl2an |
|
74 |
|
sbth |
|
75 |
67 73 74
|
syl2anc |
|
76 |
|
simpll |
|
77 |
|
fofinf1o |
|
78 |
58 75 76 77
|
syl3anc |
|
79 |
|
f1of1 |
|
80 |
78 79
|
syl |
|
81 |
|
dff12 |
|
82 |
81
|
simprbi |
|
83 |
22
|
mobidv |
|
84 |
29 30 31
|
cbvmow |
|
85 |
83 84
|
syl6bb |
|
86 |
85
|
cbvalvw |
|
87 |
82 86
|
sylib |
|
88 |
|
mormo |
|
89 |
88
|
alimi |
|
90 |
|
alral |
|
91 |
80 87 89 90
|
4syl |
|
92 |
18
|
rmobidva |
|
93 |
92
|
ralbiia |
|
94 |
91 93
|
sylibr |
|
95 |
94
|
ex |
|
96 |
95
|
pm4.71d |
|
97 |
|
reu5 |
|
98 |
97
|
ralbii |
|
99 |
|
r19.26 |
|
100 |
98 99
|
bitri |
|
101 |
96 100
|
bitr4di |
|