Step |
Hyp |
Ref |
Expression |
1 |
|
fveq2 |
|
2 |
1
|
rneqd |
|
3 |
2
|
eleq2d |
|
4 |
3
|
imbi1d |
|
5 |
4
|
imbi2d |
|
6 |
|
fveq2 |
|
7 |
6
|
rneqd |
|
8 |
7
|
eleq2d |
|
9 |
8
|
imbi1d |
|
10 |
9
|
imbi2d |
|
11 |
|
fveq2 |
|
12 |
11
|
rneqd |
|
13 |
12
|
eleq2d |
|
14 |
13
|
imbi1d |
|
15 |
14
|
imbi2d |
|
16 |
|
fveq2 |
|
17 |
16
|
rneqd |
|
18 |
17
|
eleq2d |
|
19 |
18
|
imbi1d |
|
20 |
19
|
imbi2d |
|
21 |
|
eqid |
|
22 |
21
|
satfv0 |
|
23 |
22
|
rneqd |
|
24 |
23
|
eleq2d |
|
25 |
|
rnopab |
|
26 |
25
|
eleq2i |
|
27 |
|
vex |
|
28 |
|
eqeq1 |
|
29 |
28
|
anbi2d |
|
30 |
29
|
2rexbidv |
|
31 |
30
|
exbidv |
|
32 |
27 31
|
elab |
|
33 |
|
ovex |
|
34 |
|
ssrab2 |
|
35 |
33 34
|
elpwi2 |
|
36 |
|
eleq1 |
|
37 |
35 36
|
mpbiri |
|
38 |
37
|
adantl |
|
39 |
38
|
a1i |
|
40 |
39
|
rexlimivv |
|
41 |
40
|
exlimiv |
|
42 |
32 41
|
sylbi |
|
43 |
42
|
a1i |
|
44 |
26 43
|
syl5bi |
|
45 |
24 44
|
sylbid |
|
46 |
21
|
satfvsuc |
|
47 |
46
|
3expa |
|
48 |
47
|
rneqd |
|
49 |
|
rnun |
|
50 |
48 49
|
eqtrdi |
|
51 |
50
|
eleq2d |
|
52 |
|
elun |
|
53 |
|
rnopab |
|
54 |
53
|
eleq2i |
|
55 |
|
eqeq1 |
|
56 |
55
|
anbi2d |
|
57 |
56
|
rexbidv |
|
58 |
|
eqeq1 |
|
59 |
58
|
anbi2d |
|
60 |
59
|
rexbidv |
|
61 |
57 60
|
orbi12d |
|
62 |
61
|
rexbidv |
|
63 |
62
|
exbidv |
|
64 |
27 63
|
elab |
|
65 |
54 64
|
bitri |
|
66 |
65
|
orbi2i |
|
67 |
52 66
|
bitri |
|
68 |
51 67
|
syl6bb |
|
69 |
68
|
expcom |
|
70 |
69
|
adantr |
|
71 |
70
|
imp |
|
72 |
|
simpr |
|
73 |
72
|
imp |
|
74 |
|
difss |
|
75 |
33 74
|
elpwi2 |
|
76 |
|
eleq1 |
|
77 |
75 76
|
mpbiri |
|
78 |
77
|
adantl |
|
79 |
78
|
adantl |
|
80 |
79
|
rexlimiva |
|
81 |
|
ssrab2 |
|
82 |
33 81
|
elpwi2 |
|
83 |
|
eleq1 |
|
84 |
82 83
|
mpbiri |
|
85 |
84
|
adantl |
|
86 |
85
|
a1i |
|
87 |
86
|
rexlimiv |
|
88 |
80 87
|
jaoi |
|
89 |
88
|
a1i |
|
90 |
89
|
rexlimiv |
|
91 |
90
|
exlimiv |
|
92 |
91
|
a1i |
|
93 |
73 92
|
jaod |
|
94 |
71 93
|
sylbid |
|
95 |
94
|
exp31 |
|
96 |
5 10 15 20 45 95
|
finds |
|
97 |
96
|
com12 |
|
98 |
97
|
3impia |
|
99 |
98
|
ssrdv |
|