Step |
Hyp |
Ref |
Expression |
1 |
|
scutcl |
|
2 |
1
|
ad3antrrr |
|
3 |
|
scutcl |
|
4 |
3
|
ad3antlr |
|
5 |
|
ssltss2 |
|
6 |
5
|
ad2antlr |
|
7 |
6
|
sselda |
|
8 |
|
simplr |
|
9 |
|
scutcut |
|
10 |
9
|
simp3d |
|
11 |
10
|
ad2antlr |
|
12 |
|
ssltsep |
|
13 |
11 12
|
syl |
|
14 |
|
ovex |
|
15 |
|
breq1 |
|
16 |
15
|
ralbidv |
|
17 |
14 16
|
ralsn |
|
18 |
13 17
|
sylib |
|
19 |
18
|
r19.21bi |
|
20 |
2 4 7 8 19
|
slelttrd |
|
21 |
20
|
ralrimiva |
|
22 |
|
ssltss1 |
|
23 |
22
|
adantr |
|
24 |
23
|
adantr |
|
25 |
24
|
sselda |
|
26 |
1
|
ad3antrrr |
|
27 |
3
|
ad3antlr |
|
28 |
|
scutcut |
|
29 |
28
|
simp2d |
|
30 |
29
|
adantr |
|
31 |
30
|
adantr |
|
32 |
|
ssltsep |
|
33 |
31 32
|
syl |
|
34 |
33
|
r19.21bi |
|
35 |
|
ovex |
|
36 |
|
breq2 |
|
37 |
35 36
|
ralsn |
|
38 |
34 37
|
sylib |
|
39 |
|
simplr |
|
40 |
25 26 27 38 39
|
sltletrd |
|
41 |
40
|
ralrimiva |
|
42 |
21 41
|
jca |
|
43 |
|
bdayelon |
|
44 |
43
|
onordi |
|
45 |
|
ordn2lp |
|
46 |
44 45
|
ax-mp |
|
47 |
3
|
ad2antlr |
|
48 |
1
|
adantr |
|
49 |
48
|
adantr |
|
50 |
|
sltnle |
|
51 |
47 49 50
|
syl2anc |
|
52 |
3
|
ad3antlr |
|
53 |
|
ssltex1 |
|
54 |
53
|
ad3antrrr |
|
55 |
|
snex |
|
56 |
54 55
|
jctir |
|
57 |
22
|
ad3antrrr |
|
58 |
52
|
snssd |
|
59 |
|
simplrr |
|
60 |
|
breq2 |
|
61 |
14 60
|
ralsn |
|
62 |
61
|
ralbii |
|
63 |
59 62
|
sylibr |
|
64 |
57 58 63
|
3jca |
|
65 |
|
brsslt |
|
66 |
56 64 65
|
sylanbrc |
|
67 |
|
ssltex2 |
|
68 |
67
|
ad3antrrr |
|
69 |
68 55
|
jctil |
|
70 |
|
ssltss2 |
|
71 |
70
|
ad3antrrr |
|
72 |
52
|
adantr |
|
73 |
48
|
ad3antrrr |
|
74 |
71
|
sselda |
|
75 |
|
simplr |
|
76 |
28
|
simp3d |
|
77 |
76
|
ad3antrrr |
|
78 |
|
ssltsep |
|
79 |
77 78
|
syl |
|
80 |
|
breq1 |
|
81 |
80
|
ralbidv |
|
82 |
35 81
|
ralsn |
|
83 |
79 82
|
sylib |
|
84 |
83
|
r19.21bi |
|
85 |
72 73 74 75 84
|
slttrd |
|
86 |
85
|
ralrimiva |
|
87 |
|
breq1 |
|
88 |
87
|
ralbidv |
|
89 |
14 88
|
ralsn |
|
90 |
86 89
|
sylibr |
|
91 |
58 71 90
|
3jca |
|
92 |
|
brsslt |
|
93 |
69 91 92
|
sylanbrc |
|
94 |
|
sltirr |
|
95 |
49 94
|
syl |
|
96 |
|
breq1 |
|
97 |
96
|
notbid |
|
98 |
95 97
|
syl5ibcom |
|
99 |
98
|
necon2ad |
|
100 |
99
|
imp |
|
101 |
100
|
necomd |
|
102 |
|
scutbdaylt |
|
103 |
52 66 93 101 102
|
syl121anc |
|
104 |
1
|
ad3antrrr |
|
105 |
|
ssltex1 |
|
106 |
105
|
ad3antlr |
|
107 |
|
snex |
|
108 |
106 107
|
jctir |
|
109 |
|
ssltss1 |
|
110 |
109
|
ad3antlr |
|
111 |
104
|
snssd |
|
112 |
110
|
sselda |
|
113 |
52
|
adantr |
|
114 |
48
|
ad3antrrr |
|
115 |
9
|
simp2d |
|
116 |
115
|
ad3antlr |
|
117 |
|
ssltsep |
|
118 |
116 117
|
syl |
|
119 |
118
|
r19.21bi |
|
120 |
|
breq2 |
|
121 |
14 120
|
ralsn |
|
122 |
119 121
|
sylib |
|
123 |
|
simplr |
|
124 |
112 113 114 122 123
|
slttrd |
|
125 |
|
breq2 |
|
126 |
35 125
|
ralsn |
|
127 |
124 126
|
sylibr |
|
128 |
127
|
ralrimiva |
|
129 |
110 111 128
|
3jca |
|
130 |
|
brsslt |
|
131 |
108 129 130
|
sylanbrc |
|
132 |
|
ssltex2 |
|
133 |
132
|
ad3antlr |
|
134 |
133 107
|
jctil |
|
135 |
5
|
ad3antlr |
|
136 |
|
simplrl |
|
137 |
|
breq1 |
|
138 |
137
|
ralbidv |
|
139 |
35 138
|
ralsn |
|
140 |
136 139
|
sylibr |
|
141 |
111 135 140
|
3jca |
|
142 |
|
brsslt |
|
143 |
134 141 142
|
sylanbrc |
|
144 |
|
scutbdaylt |
|
145 |
104 131 143 100 144
|
syl121anc |
|
146 |
103 145
|
jca |
|
147 |
146
|
ex |
|
148 |
51 147
|
sylbird |
|
149 |
46 148
|
mt3i |
|
150 |
42 149
|
impbida |
|
151 |
|
breq12 |
|
152 |
|
breq1 |
|
153 |
152
|
ralbidv |
|
154 |
|
breq2 |
|
155 |
154
|
ralbidv |
|
156 |
153 155
|
bi2anan9 |
|
157 |
151 156
|
bibi12d |
|
158 |
150 157
|
syl5ibr |
|
159 |
158
|
impcom |
|