Step |
Hyp |
Ref |
Expression |
1 |
|
sltso |
|
2 |
|
simp11 |
|
3 |
|
sonr |
|
4 |
1 2 3
|
sylancr |
|
5 |
|
simpl2r |
|
6 |
|
simpl2l |
|
7 |
|
simpl11 |
|
8 |
|
nofun |
|
9 |
|
funrel |
|
10 |
8 9
|
syl |
|
11 |
7 10
|
syl |
|
12 |
|
simpl13 |
|
13 |
|
simpr |
|
14 |
|
nolt02olem |
|
15 |
7 12 13 14
|
syl3anc |
|
16 |
|
relssres |
|
17 |
11 15 16
|
syl2anc |
|
18 |
|
simpl12 |
|
19 |
|
nofun |
|
20 |
|
funrel |
|
21 |
19 20
|
syl |
|
22 |
18 21
|
syl |
|
23 |
|
simpl3 |
|
24 |
|
nolt02olem |
|
25 |
18 12 23 24
|
syl3anc |
|
26 |
|
relssres |
|
27 |
22 25 26
|
syl2anc |
|
28 |
6 17 27
|
3eqtr3d |
|
29 |
5 28
|
breqtrrd |
|
30 |
4 29
|
mtand |
|
31 |
|
simp2r |
|
32 |
|
simp12 |
|
33 |
|
sltval |
|
34 |
2 32 33
|
syl2anc |
|
35 |
31 34
|
mpbid |
|
36 |
|
ralinexa |
|
37 |
36
|
con2bii |
|
38 |
35 37
|
sylib |
|
39 |
|
1n0 |
|
40 |
39
|
neii |
|
41 |
|
eqtr2 |
|
42 |
40 41
|
mto |
|
43 |
|
df-2o |
|
44 |
|
2on |
|
45 |
43 44
|
eqeltrri |
|
46 |
45
|
onordi |
|
47 |
|
1oex |
|
48 |
47
|
sucid |
|
49 |
|
nordeq |
|
50 |
46 48 49
|
mp2an |
|
51 |
43 50
|
eqnetri |
|
52 |
51
|
nesymi |
|
53 |
|
eqtr2 |
|
54 |
52 53
|
mto |
|
55 |
|
2on0 |
|
56 |
55
|
nesymi |
|
57 |
|
eqtr2 |
|
58 |
56 57
|
mto |
|
59 |
42 54 58
|
3pm3.2i |
|
60 |
|
fvex |
|
61 |
60 60
|
brtp |
|
62 |
|
3oran |
|
63 |
61 62
|
bitri |
|
64 |
63
|
con2bii |
|
65 |
59 64
|
mpbi |
|
66 |
|
simpl2l |
|
67 |
66
|
adantr |
|
68 |
67
|
fveq1d |
|
69 |
68
|
breq2d |
|
70 |
65 69
|
mtbii |
|
71 |
|
fvres |
|
72 |
|
fvres |
|
73 |
71 72
|
breq12d |
|
74 |
73
|
notbid |
|
75 |
70 74
|
syl5ibcom |
|
76 |
51
|
neii |
|
77 |
76
|
intnanr |
|
78 |
56
|
intnan |
|
79 |
56
|
intnan |
|
80 |
77 78 79
|
3pm3.2i |
|
81 |
|
2oex |
|
82 |
|
0ex |
|
83 |
81 82
|
brtp |
|
84 |
|
3oran |
|
85 |
83 84
|
bitri |
|
86 |
85
|
con2bii |
|
87 |
80 86
|
mpbi |
|
88 |
|
simplr |
|
89 |
|
simpll3 |
|
90 |
88 89
|
breq12d |
|
91 |
87 90
|
mtbiri |
|
92 |
|
fveq2 |
|
93 |
|
fveq2 |
|
94 |
92 93
|
breq12d |
|
95 |
94
|
notbid |
|
96 |
91 95
|
syl5ibrcom |
|
97 |
|
fveq2 |
|
98 |
|
fveq2 |
|
99 |
97 98
|
eqeq12d |
|
100 |
99
|
rspccv |
|
101 |
100
|
ad2antll |
|
102 |
|
eqcom |
|
103 |
101 102
|
syl6ib |
|
104 |
89 88
|
eqeq12d |
|
105 |
103 104
|
sylibd |
|
106 |
56 105
|
mtoi |
|
107 |
|
simprl |
|
108 |
|
simpl13 |
|
109 |
108
|
adantr |
|
110 |
|
ontri1 |
|
111 |
|
onsseleq |
|
112 |
110 111
|
bitr3d |
|
113 |
107 109 112
|
syl2anc |
|
114 |
106 113
|
mpbid |
|
115 |
75 96 114
|
mpjaod |
|
116 |
115
|
expr |
|
117 |
116
|
ralrimiva |
|
118 |
38 117
|
mtand |
|
119 |
|
nofv |
|
120 |
2 119
|
syl |
|
121 |
|
3orcoma |
|
122 |
120 121
|
sylib |
|
123 |
30 118 122
|
ecase23d |
|