Step |
Hyp |
Ref |
Expression |
1 |
|
ssltss1 |
|
2 |
|
ssltex1 |
|
3 |
|
ssltss2 |
|
4 |
|
ssltex2 |
|
5 |
|
ssltsep |
|
6 |
|
noeta2 |
|
7 |
1 2 3 4 5 6
|
syl221anc |
|
8 |
|
3simpa |
|
9 |
2
|
ad2antrr |
|
10 |
|
snex |
|
11 |
9 10
|
jctir |
|
12 |
1
|
ad2antrr |
|
13 |
|
snssi |
|
14 |
13
|
adantl |
|
15 |
14
|
adantr |
|
16 |
|
vex |
|
17 |
|
breq2 |
|
18 |
16 17
|
ralsn |
|
19 |
18
|
ralbii |
|
20 |
19
|
biimpri |
|
21 |
20
|
adantl |
|
22 |
12 15 21
|
3jca |
|
23 |
|
brsslt |
|
24 |
11 22 23
|
sylanbrc |
|
25 |
24
|
ex |
|
26 |
4
|
ad2antrr |
|
27 |
26 10
|
jctil |
|
28 |
14
|
adantr |
|
29 |
3
|
ad2antrr |
|
30 |
|
ralcom |
|
31 |
|
breq1 |
|
32 |
16 31
|
ralsn |
|
33 |
32
|
ralbii |
|
34 |
30 33
|
sylbbr |
|
35 |
34
|
adantl |
|
36 |
28 29 35
|
3jca |
|
37 |
|
brsslt |
|
38 |
27 36 37
|
sylanbrc |
|
39 |
38
|
ex |
|
40 |
25 39
|
anim12d |
|
41 |
8 40
|
syl5 |
|
42 |
41
|
reximdva |
|
43 |
7 42
|
mpd |
|
44 |
|
rabn0 |
|
45 |
43 44
|
sylibr |
|
46 |
|
ssrab2 |
|
47 |
46
|
a1i |
|
48 |
|
simplr3 |
|
49 |
2
|
ad2antrr |
|
50 |
|
snex |
|
51 |
49 50
|
jctir |
|
52 |
1
|
ad2antrr |
|
53 |
|
snssi |
|
54 |
48 53
|
syl |
|
55 |
52
|
sselda |
|
56 |
|
simplr1 |
|
57 |
56
|
adantr |
|
58 |
48
|
adantr |
|
59 |
|
simplll |
|
60 |
59
|
adantl |
|
61 |
|
ssltsep |
|
62 |
60 61
|
syl |
|
63 |
62
|
r19.21bi |
|
64 |
|
vex |
|
65 |
|
breq2 |
|
66 |
64 65
|
ralsn |
|
67 |
63 66
|
sylib |
|
68 |
|
simprrl |
|
69 |
68
|
adantr |
|
70 |
55 57 58 67 69
|
slttrd |
|
71 |
|
vex |
|
72 |
|
breq2 |
|
73 |
71 72
|
ralsn |
|
74 |
70 73
|
sylibr |
|
75 |
74
|
ralrimiva |
|
76 |
52 54 75
|
3jca |
|
77 |
|
brsslt |
|
78 |
51 76 77
|
sylanbrc |
|
79 |
4
|
ad2antrr |
|
80 |
79 50
|
jctil |
|
81 |
3
|
ad2antrr |
|
82 |
48
|
adantr |
|
83 |
|
simplr2 |
|
84 |
83
|
adantr |
|
85 |
81
|
sselda |
|
86 |
|
simprrr |
|
87 |
86
|
adantr |
|
88 |
|
simplrr |
|
89 |
88
|
adantl |
|
90 |
|
ssltsep |
|
91 |
89 90
|
syl |
|
92 |
|
vex |
|
93 |
|
breq1 |
|
94 |
93
|
ralbidv |
|
95 |
92 94
|
ralsn |
|
96 |
91 95
|
sylib |
|
97 |
96
|
r19.21bi |
|
98 |
82 84 85 87 97
|
slttrd |
|
99 |
98
|
ralrimiva |
|
100 |
|
breq1 |
|
101 |
100
|
ralbidv |
|
102 |
71 101
|
ralsn |
|
103 |
99 102
|
sylibr |
|
104 |
54 81 103
|
3jca |
|
105 |
|
brsslt |
|
106 |
80 104 105
|
sylanbrc |
|
107 |
48 78 106
|
jca32 |
|
108 |
107
|
exp44 |
|
109 |
108
|
ralrimivvva |
|
110 |
|
sneq |
|
111 |
110
|
breq2d |
|
112 |
110
|
breq1d |
|
113 |
111 112
|
anbi12d |
|
114 |
113
|
ralrab |
|
115 |
|
sneq |
|
116 |
115
|
breq2d |
|
117 |
115
|
breq1d |
|
118 |
116 117
|
anbi12d |
|
119 |
118
|
ralrab |
|
120 |
|
sneq |
|
121 |
120
|
breq2d |
|
122 |
120
|
breq1d |
|
123 |
121 122
|
anbi12d |
|
124 |
123
|
elrab |
|
125 |
124
|
imbi2i |
|
126 |
125
|
ralbii |
|
127 |
126
|
ralbii |
|
128 |
|
r19.21v |
|
129 |
128
|
ralbii |
|
130 |
119 127 129
|
3bitr4i |
|
131 |
130
|
ralbii |
|
132 |
|
r19.21v |
|
133 |
132
|
ralbii |
|
134 |
|
r19.21v |
|
135 |
133 134
|
bitri |
|
136 |
135
|
ralbii |
|
137 |
114 131 136
|
3bitr4i |
|
138 |
109 137
|
sylibr |
|
139 |
|
nocvxmin |
|
140 |
45 47 138 139
|
syl3anc |
|