Step |
Hyp |
Ref |
Expression |
1 |
|
eqeq1 |
|
2 |
1
|
rexbidv |
|
3 |
2
|
elrab |
|
4 |
|
simp-4l |
|
5 |
|
simpr |
|
6 |
4 5
|
sseldd |
|
7 |
6
|
recnd |
|
8 |
|
simp-4r |
|
9 |
8
|
recnd |
|
10 |
7 9
|
subcld |
|
11 |
|
simprr |
|
12 |
11
|
ad2antrr |
|
13 |
|
nelneq |
|
14 |
5 12 13
|
syl2anc |
|
15 |
|
subeq0 |
|
16 |
15
|
necon3abid |
|
17 |
7 9 16
|
syl2anc |
|
18 |
14 17
|
mpbird |
|
19 |
10 18
|
absrpcld |
|
20 |
|
eleq1 |
|
21 |
19 20
|
syl5ibrcom |
|
22 |
21
|
rexlimdva |
|
23 |
22
|
expimpd |
|
24 |
3 23
|
syl5bi |
|
25 |
24
|
ssrdv |
|
26 |
25
|
adantr |
|
27 |
|
abrexfi |
|
28 |
|
rabssab |
|
29 |
|
ssfi |
|
30 |
27 28 29
|
sylancl |
|
31 |
30
|
adantl |
|
32 |
|
simplrl |
|
33 |
|
n0 |
|
34 |
32 33
|
sylib |
|
35 |
|
simp-4l |
|
36 |
|
simpr |
|
37 |
35 36
|
sseldd |
|
38 |
37
|
recnd |
|
39 |
|
simp-4r |
|
40 |
39
|
recnd |
|
41 |
38 40
|
subcld |
|
42 |
41
|
abscld |
|
43 |
|
eqid |
|
44 |
|
fvoveq1 |
|
45 |
44
|
rspceeqv |
|
46 |
43 45
|
mpan2 |
|
47 |
46
|
adantl |
|
48 |
|
eqeq1 |
|
49 |
48
|
rexbidv |
|
50 |
49
|
elrab |
|
51 |
42 47 50
|
sylanbrc |
|
52 |
51
|
ne0d |
|
53 |
34 52
|
exlimddv |
|
54 |
|
ssrab2 |
|
55 |
54
|
a1i |
|
56 |
|
gtso |
|
57 |
|
fisupcl |
|
58 |
56 57
|
mpan |
|
59 |
31 53 55 58
|
syl3anc |
|
60 |
26 59
|
sseldd |
|
61 |
54
|
a1i |
|
62 |
|
soss |
|
63 |
54 56 62
|
mp2 |
|
64 |
63
|
a1i |
|
65 |
|
fisupg |
|
66 |
64 31 53 65
|
syl3anc |
|
67 |
|
elrabi |
|
68 |
|
elrabi |
|
69 |
|
vex |
|
70 |
|
vex |
|
71 |
69 70
|
brcnv |
|
72 |
71
|
notbii |
|
73 |
|
lenlt |
|
74 |
73
|
biimprd |
|
75 |
72 74
|
syl5bi |
|
76 |
75
|
adantll |
|
77 |
68 76
|
sylan2 |
|
78 |
77
|
ralimdva |
|
79 |
78
|
adantrd |
|
80 |
67 79
|
sylan2 |
|
81 |
80
|
reximdva |
|
82 |
66 81
|
mpd |
|
83 |
82
|
adantr |
|
84 |
|
lbinfle |
|
85 |
61 83 51 84
|
syl3anc |
|
86 |
|
df-inf |
|
87 |
86
|
eqcomi |
|
88 |
87
|
breq1i |
|
89 |
85 88
|
sylibr |
|
90 |
54 59
|
sseldi |
|
91 |
90
|
adantr |
|
92 |
91 42
|
lenltd |
|
93 |
89 92
|
mpbid |
|
94 |
93
|
ralrimiva |
|
95 |
|
breq2 |
|
96 |
95
|
notbid |
|
97 |
96
|
ralbidv |
|
98 |
97
|
rspcev |
|
99 |
60 94 98
|
syl2anc |
|
100 |
|
ralnex |
|
101 |
100
|
rexbii |
|
102 |
|
rexnal |
|
103 |
101 102
|
bitri |
|
104 |
99 103
|
sylib |
|
105 |
104
|
ex |
|
106 |
105
|
3impa |
|
107 |
106
|
con2d |
|
108 |
107
|
imp |
|