Step |
Hyp |
Ref |
Expression |
1 |
|
sltval |
|
2 |
|
fvex |
|
3 |
|
fvex |
|
4 |
2 3
|
brtp |
|
5 |
|
1n0 |
|
6 |
5
|
neii |
|
7 |
|
eqeq1 |
|
8 |
6 7
|
mtbiri |
|
9 |
|
fvprc |
|
10 |
8 9
|
nsyl2 |
|
11 |
10
|
adantr |
|
12 |
10
|
adantr |
|
13 |
|
2on0 |
|
14 |
13
|
neii |
|
15 |
|
eqeq1 |
|
16 |
14 15
|
mtbiri |
|
17 |
|
fvprc |
|
18 |
16 17
|
nsyl2 |
|
19 |
18
|
adantl |
|
20 |
11 12 19
|
3jaoi |
|
21 |
4 20
|
sylbi |
|
22 |
|
onintrab |
|
23 |
21 22
|
sylib |
|
24 |
23
|
adantl |
|
25 |
|
onelon |
|
26 |
25
|
expcom |
|
27 |
24 26
|
syl5 |
|
28 |
|
fveq2 |
|
29 |
|
fveq2 |
|
30 |
28 29
|
neeq12d |
|
31 |
30
|
onnminsb |
|
32 |
31
|
com12 |
|
33 |
27 32
|
syldc |
|
34 |
|
df-ne |
|
35 |
34
|
con2bii |
|
36 |
33 35
|
syl6ibr |
|
37 |
36
|
ralrimiv |
|
38 |
24 37
|
jca |
|
39 |
38
|
ex |
|
40 |
39
|
impac |
|
41 |
|
anass |
|
42 |
40 41
|
sylib |
|
43 |
|
raleq |
|
44 |
|
fveq2 |
|
45 |
|
fveq2 |
|
46 |
44 45
|
breq12d |
|
47 |
43 46
|
anbi12d |
|
48 |
47
|
rspcev |
|
49 |
42 48
|
syl |
|
50 |
49
|
ex |
|
51 |
|
eqeq12 |
|
52 |
6 51
|
mtbiri |
|
53 |
|
1on |
|
54 |
|
0elon |
|
55 |
|
suc11 |
|
56 |
55
|
necon3bid |
|
57 |
53 54 56
|
mp2an |
|
58 |
5 57
|
mpbir |
|
59 |
|
df-2o |
|
60 |
|
df-1o |
|
61 |
59 60
|
eqeq12i |
|
62 |
58 61
|
nemtbir |
|
63 |
|
eqeq12 |
|
64 |
|
eqcom |
|
65 |
63 64
|
syl6bb |
|
66 |
62 65
|
mtbiri |
|
67 |
13
|
nesymi |
|
68 |
|
eqeq12 |
|
69 |
67 68
|
mtbiri |
|
70 |
52 66 69
|
3jaoi |
|
71 |
|
fvex |
|
72 |
|
fvex |
|
73 |
71 72
|
brtp |
|
74 |
|
df-ne |
|
75 |
70 73 74
|
3imtr4i |
|
76 |
|
fveq2 |
|
77 |
|
fveq2 |
|
78 |
76 77
|
neeq12d |
|
79 |
78
|
elrab |
|
80 |
79
|
biimpri |
|
81 |
80
|
adantlr |
|
82 |
|
ssrab2 |
|
83 |
|
ne0i |
|
84 |
83
|
adantl |
|
85 |
|
onint |
|
86 |
82 84 85
|
sylancr |
|
87 |
|
nfrab1 |
|
88 |
87
|
nfint |
|
89 |
|
nfcv |
|
90 |
|
nfcv |
|
91 |
90 88
|
nffv |
|
92 |
|
nfcv |
|
93 |
92 88
|
nffv |
|
94 |
91 93
|
nfne |
|
95 |
|
fveq2 |
|
96 |
|
fveq2 |
|
97 |
95 96
|
neeq12d |
|
98 |
88 89 94 97
|
elrabf |
|
99 |
98
|
simprbi |
|
100 |
86 99
|
syl |
|
101 |
|
df-ne |
|
102 |
100 101
|
sylib |
|
103 |
|
fveq2 |
|
104 |
|
fveq2 |
|
105 |
103 104
|
eqeq12d |
|
106 |
105
|
rspccv |
|
107 |
106
|
ad2antlr |
|
108 |
102 107
|
mtod |
|
109 |
|
simpll |
|
110 |
|
oninton |
|
111 |
82 83 110
|
sylancr |
|
112 |
111
|
adantl |
|
113 |
|
ontri1 |
|
114 |
109 112 113
|
syl2anc |
|
115 |
108 114
|
mpbird |
|
116 |
|
intss1 |
|
117 |
116
|
adantl |
|
118 |
115 117
|
eqssd |
|
119 |
81 118
|
syldan |
|
120 |
75 119
|
sylan2 |
|
121 |
120
|
fveq2d |
|
122 |
120
|
fveq2d |
|
123 |
121 122
|
breq12d |
|
124 |
123
|
biimpd |
|
125 |
124
|
ex |
|
126 |
125
|
pm2.43d |
|
127 |
126
|
expimpd |
|
128 |
127
|
rexlimiv |
|
129 |
50 128
|
impbid1 |
|
130 |
1 129
|
bitr4d |
|