Step |
Hyp |
Ref |
Expression |
1 |
|
fveq2 |
|
2 |
1
|
eleq2d |
|
3 |
2
|
notbid |
|
4 |
|
fveq2 |
|
5 |
4
|
eleq2d |
|
6 |
5
|
notbid |
|
7 |
|
fveq2 |
|
8 |
7
|
eleq2d |
|
9 |
8
|
notbid |
|
10 |
|
fveq2 |
|
11 |
10
|
eleq2d |
|
12 |
11
|
notbid |
|
13 |
|
0ex |
|
14 |
|
opex |
|
15 |
13 14
|
pm3.2i |
|
16 |
15
|
a1i |
|
17 |
|
necom |
|
18 |
|
opnz |
|
19 |
17 18
|
bitri |
|
20 |
16 19
|
sylibr |
|
21 |
20
|
neneqd |
|
22 |
|
goel |
|
23 |
22
|
eqeq2d |
|
24 |
21 23
|
mtbird |
|
25 |
24
|
rgen2 |
|
26 |
|
ralnex2 |
|
27 |
25 26
|
mpbi |
|
28 |
27
|
intnan |
|
29 |
|
fmla0 |
|
30 |
29
|
eleq2i |
|
31 |
|
eqeq1 |
|
32 |
31
|
2rexbidv |
|
33 |
32
|
elrab |
|
34 |
30 33
|
bitri |
|
35 |
28 34
|
mtbir |
|
36 |
|
simpr |
|
37 |
|
1oex |
|
38 |
|
opex |
|
39 |
37 38
|
opnzi |
|
40 |
39
|
nesymi |
|
41 |
|
gonafv |
|
42 |
41
|
adantll |
|
43 |
42
|
eqeq2d |
|
44 |
40 43
|
mtbiri |
|
45 |
44
|
ralrimiva |
|
46 |
|
2oex |
|
47 |
|
opex |
|
48 |
46 47
|
opnzi |
|
49 |
48
|
nesymi |
|
50 |
|
df-goal |
|
51 |
50
|
eqeq2i |
|
52 |
49 51
|
mtbir |
|
53 |
52
|
a1i |
|
54 |
53
|
ralrimiva |
|
55 |
45 54
|
jca |
|
56 |
55
|
ralrimiva |
|
57 |
56
|
adantr |
|
58 |
|
ralnex |
|
59 |
|
ralnex |
|
60 |
58 59
|
anbi12i |
|
61 |
|
ioran |
|
62 |
60 61
|
bitr4i |
|
63 |
62
|
ralbii |
|
64 |
|
ralnex |
|
65 |
63 64
|
bitri |
|
66 |
57 65
|
sylib |
|
67 |
|
ioran |
|
68 |
36 66 67
|
sylanbrc |
|
69 |
|
fmlasuc |
|
70 |
69
|
eleq2d |
|
71 |
|
elun |
|
72 |
|
eqeq1 |
|
73 |
72
|
rexbidv |
|
74 |
|
eqeq1 |
|
75 |
74
|
rexbidv |
|
76 |
73 75
|
orbi12d |
|
77 |
76
|
rexbidv |
|
78 |
13 77
|
elab |
|
79 |
78
|
orbi2i |
|
80 |
71 79
|
bitri |
|
81 |
70 80
|
bitrdi |
|
82 |
81
|
adantr |
|
83 |
68 82
|
mtbird |
|
84 |
83
|
ex |
|
85 |
3 6 9 12 35 84
|
finds |
|
86 |
|
df-nel |
|
87 |
85 86
|
sylibr |
|