Step |
Hyp |
Ref |
Expression |
1 |
|
ac6sfi.1 |
|
2 |
|
raleq |
|
3 |
|
feq2 |
|
4 |
|
raleq |
|
5 |
3 4
|
anbi12d |
|
6 |
5
|
exbidv |
|
7 |
2 6
|
imbi12d |
|
8 |
|
raleq |
|
9 |
|
feq2 |
|
10 |
|
raleq |
|
11 |
9 10
|
anbi12d |
|
12 |
11
|
exbidv |
|
13 |
8 12
|
imbi12d |
|
14 |
|
raleq |
|
15 |
|
feq2 |
|
16 |
|
raleq |
|
17 |
15 16
|
anbi12d |
|
18 |
17
|
exbidv |
|
19 |
|
feq1 |
|
20 |
|
fvex |
|
21 |
20 1
|
sbcie |
|
22 |
|
fveq1 |
|
23 |
22
|
sbceq1d |
|
24 |
21 23
|
bitr3id |
|
25 |
24
|
ralbidv |
|
26 |
19 25
|
anbi12d |
|
27 |
26
|
cbvexvw |
|
28 |
18 27
|
bitrdi |
|
29 |
14 28
|
imbi12d |
|
30 |
|
raleq |
|
31 |
|
feq2 |
|
32 |
|
raleq |
|
33 |
31 32
|
anbi12d |
|
34 |
33
|
exbidv |
|
35 |
30 34
|
imbi12d |
|
36 |
|
f0 |
|
37 |
|
0ex |
|
38 |
|
ral0 |
|
39 |
38
|
biantru |
|
40 |
|
feq1 |
|
41 |
39 40
|
bitr3id |
|
42 |
37 41
|
spcev |
|
43 |
36 42
|
mp1i |
|
44 |
|
ssun1 |
|
45 |
|
ssralv |
|
46 |
44 45
|
ax-mp |
|
47 |
46
|
imim1i |
|
48 |
|
ssun2 |
|
49 |
|
ssralv |
|
50 |
48 49
|
ax-mp |
|
51 |
|
ralsnsg |
|
52 |
51
|
elv |
|
53 |
|
sbcrex |
|
54 |
52 53
|
bitri |
|
55 |
50 54
|
sylib |
|
56 |
|
nfv |
|
57 |
|
nfv |
|
58 |
|
nfv |
|
59 |
|
nfcv |
|
60 |
|
nfsbc1v |
|
61 |
59 60
|
nfralw |
|
62 |
58 61
|
nfan |
|
63 |
62
|
nfex |
|
64 |
57 63
|
nfim |
|
65 |
|
simprl |
|
66 |
|
vex |
|
67 |
|
vex |
|
68 |
66 67
|
f1osn |
|
69 |
|
f1of |
|
70 |
68 69
|
mp1i |
|
71 |
|
simpl2 |
|
72 |
71
|
snssd |
|
73 |
70 72
|
fssd |
|
74 |
|
simpl1 |
|
75 |
|
disjsn |
|
76 |
74 75
|
sylibr |
|
77 |
65 73 76
|
fun2d |
|
78 |
|
simprr |
|
79 |
|
eleq1a |
|
80 |
79
|
necon3bd |
|
81 |
80
|
impcom |
|
82 |
|
fvunsn |
|
83 |
|
dfsbcq |
|
84 |
83 21
|
bitr2di |
|
85 |
81 82 84
|
3syl |
|
86 |
85
|
ralbidva |
|
87 |
74 86
|
syl |
|
88 |
78 87
|
mpbid |
|
89 |
|
simpl3 |
|
90 |
|
ffun |
|
91 |
|
ssun2 |
|
92 |
|
vsnid |
|
93 |
67
|
dmsnop |
|
94 |
92 93
|
eleqtrri |
|
95 |
|
funssfv |
|
96 |
91 94 95
|
mp3an23 |
|
97 |
77 90 96
|
3syl |
|
98 |
66 67
|
fvsn |
|
99 |
97 98
|
eqtr2di |
|
100 |
|
ralsnsg |
|
101 |
100
|
elv |
|
102 |
|
elsni |
|
103 |
102
|
fveq2d |
|
104 |
103
|
eqeq2d |
|
105 |
104
|
biimparc |
|
106 |
|
sbceq1a |
|
107 |
105 106
|
syl |
|
108 |
107
|
ralbidva |
|
109 |
101 108
|
bitr3id |
|
110 |
99 109
|
syl |
|
111 |
89 110
|
mpbid |
|
112 |
|
ralun |
|
113 |
88 111 112
|
syl2anc |
|
114 |
|
vex |
|
115 |
|
snex |
|
116 |
114 115
|
unex |
|
117 |
|
feq1 |
|
118 |
|
fveq1 |
|
119 |
118
|
sbceq1d |
|
120 |
119
|
ralbidv |
|
121 |
117 120
|
anbi12d |
|
122 |
116 121
|
spcev |
|
123 |
77 113 122
|
syl2anc |
|
124 |
123
|
ex |
|
125 |
124
|
exlimdv |
|
126 |
125
|
3exp |
|
127 |
56 64 126
|
rexlimd |
|
128 |
55 127
|
syl5 |
|
129 |
128
|
a2d |
|
130 |
47 129
|
syl5 |
|
131 |
130
|
adantl |
|
132 |
7 13 29 35 43 131
|
findcard2s |
|
133 |
132
|
imp |
|