Step |
Hyp |
Ref |
Expression |
1 |
|
simp2 |
|
2 |
|
sucelon |
|
3 |
1 2
|
sylib |
|
4 |
|
simp1 |
|
5 |
|
on0eln0 |
|
6 |
5
|
biimpar |
|
7 |
6
|
3adant2 |
|
8 |
|
omword2 |
|
9 |
3 4 7 8
|
syl21anc |
|
10 |
|
sucidg |
|
11 |
|
ssel |
|
12 |
10 11
|
syl5 |
|
13 |
9 1 12
|
sylc |
|
14 |
|
suceq |
|
15 |
14
|
oveq2d |
|
16 |
15
|
eleq2d |
|
17 |
16
|
rspcev |
|
18 |
1 13 17
|
syl2anc |
|
19 |
|
suceq |
|
20 |
19
|
oveq2d |
|
21 |
20
|
eleq2d |
|
22 |
21
|
onminex |
|
23 |
|
vex |
|
24 |
23
|
elon |
|
25 |
|
ordzsl |
|
26 |
24 25
|
bitri |
|
27 |
|
oveq2 |
|
28 |
|
om0 |
|
29 |
27 28
|
sylan9eqr |
|
30 |
|
ne0i |
|
31 |
30
|
necon2bi |
|
32 |
29 31
|
syl |
|
33 |
32
|
ex |
|
34 |
33
|
a1d |
|
35 |
34
|
3ad2ant1 |
|
36 |
35
|
imp |
|
37 |
|
simp3 |
|
38 |
|
simp2 |
|
39 |
|
raleq |
|
40 |
|
vex |
|
41 |
40
|
sucid |
|
42 |
|
suceq |
|
43 |
42
|
oveq2d |
|
44 |
43
|
eleq2d |
|
45 |
44
|
notbid |
|
46 |
45
|
rspcv |
|
47 |
41 46
|
ax-mp |
|
48 |
39 47
|
syl6bi |
|
49 |
37 38 48
|
sylc |
|
50 |
|
oveq2 |
|
51 |
50
|
eleq2d |
|
52 |
51
|
notbid |
|
53 |
52
|
biimpar |
|
54 |
37 49 53
|
syl2anc |
|
55 |
54
|
3expia |
|
56 |
55
|
rexlimdvw |
|
57 |
|
ralnex |
|
58 |
|
simpr |
|
59 |
23
|
a1i |
|
60 |
|
simpl |
|
61 |
|
omlim |
|
62 |
58 59 60 61
|
syl12anc |
|
63 |
62
|
eleq2d |
|
64 |
|
eliun |
|
65 |
|
limord |
|
66 |
65
|
3ad2ant1 |
|
67 |
66 24
|
sylibr |
|
68 |
|
simp3 |
|
69 |
|
onelon |
|
70 |
67 68 69
|
syl2anc |
|
71 |
|
suceloni |
|
72 |
70 71
|
syl |
|
73 |
|
simp2 |
|
74 |
|
sssucid |
|
75 |
|
omwordi |
|
76 |
74 75
|
mpi |
|
77 |
70 72 73 76
|
syl3anc |
|
78 |
77
|
sseld |
|
79 |
78
|
3expia |
|
80 |
79
|
reximdvai |
|
81 |
64 80
|
syl5bi |
|
82 |
63 81
|
sylbid |
|
83 |
82
|
con3d |
|
84 |
57 83
|
syl5bi |
|
85 |
84
|
expimpd |
|
86 |
85
|
com12 |
|
87 |
86
|
3ad2antl1 |
|
88 |
36 56 87
|
3jaod |
|
89 |
26 88
|
syl5bi |
|
90 |
89
|
impr |
|
91 |
|
simpl1 |
|
92 |
|
simprr |
|
93 |
|
omcl |
|
94 |
91 92 93
|
syl2anc |
|
95 |
|
simpl2 |
|
96 |
|
ontri1 |
|
97 |
94 95 96
|
syl2anc |
|
98 |
90 97
|
mpbird |
|
99 |
|
oawordex |
|
100 |
94 95 99
|
syl2anc |
|
101 |
98 100
|
mpbid |
|
102 |
101
|
3adantr1 |
|
103 |
|
simp3r |
|
104 |
|
simp21 |
|
105 |
|
simp11 |
|
106 |
|
simp23 |
|
107 |
|
omsuc |
|
108 |
105 106 107
|
syl2anc |
|
109 |
104 108
|
eleqtrd |
|
110 |
103 109
|
eqeltrd |
|
111 |
|
simp3l |
|
112 |
105 106 93
|
syl2anc |
|
113 |
|
oaord |
|
114 |
111 105 112 113
|
syl3anc |
|
115 |
110 114
|
mpbird |
|
116 |
115 103
|
jca |
|
117 |
116
|
3expia |
|
118 |
117
|
reximdv2 |
|
119 |
102 118
|
mpd |
|
120 |
119
|
expcom |
|
121 |
120
|
3expia |
|
122 |
121
|
com13 |
|
123 |
122
|
reximdvai |
|
124 |
22 123
|
syl5 |
|
125 |
18 124
|
mpd |
|