Step | Hyp | Ref
| Expression |
1 | | undifss 3494 |
. . . . . . . 8
|
2 | 1 | biimpi 119 |
. . . . . . 7
|
3 | 2 | adantl 275 |
. . . . . 6
EXMID
|
4 | | elun1 3294 |
. . . . . . . . . . 11
|
5 | 4 | adantl 275 |
. . . . . . . . . 10
EXMID
|
6 | | simplr 525 |
. . . . . . . . . . . 12
EXMID |
7 | | simpr 109 |
. . . . . . . . . . . 12
EXMID
|
8 | 6, 7 | eldifd 3131 |
. . . . . . . . . . 11
EXMID |
9 | | elun2 3295 |
. . . . . . . . . . 11
|
10 | 8, 9 | syl 14 |
. . . . . . . . . 10
EXMID
|
11 | | exmidexmid 4180 |
. . . . . . . . . . . 12
EXMID
DECID
|
12 | | exmiddc 831 |
. . . . . . . . . . . 12
DECID
|
13 | 11, 12 | syl 14 |
. . . . . . . . . . 11
EXMID |
14 | 13 | adantr 274 |
. . . . . . . . . 10
EXMID |
15 | 5, 10, 14 | mpjaodan 793 |
. . . . . . . . 9
EXMID |
16 | 15 | ex 114 |
. . . . . . . 8
EXMID |
17 | 16 | ssrdv 3153 |
. . . . . . 7
EXMID
|
18 | 17 | adantr 274 |
. . . . . 6
EXMID
|
19 | 3, 18 | eqssd 3164 |
. . . . 5
EXMID
|
20 | 19 | ex 114 |
. . . 4
EXMID
|
21 | | ssun1 3290 |
. . . . 5
|
22 | | sseq2 3171 |
. . . . 5
|
23 | 21, 22 | mpbii 147 |
. . . 4
|
24 | 20, 23 | impbid1 141 |
. . 3
EXMID
|
25 | 24 | alrimivv 1868 |
. 2
EXMID
|
26 | | vex 2733 |
. . . . . 6
|
27 | | p0ex 4172 |
. . . . . 6
|
28 | | sseq12 3172 |
. . . . . . . 8
|
29 | | simpl 108 |
. . . . . . . . . 10
|
30 | | simpr 109 |
. . . . . . . . . . 11
|
31 | 30, 29 | difeq12d 3246 |
. . . . . . . . . 10
|
32 | 29, 31 | uneq12d 3282 |
. . . . . . . . 9
|
33 | 32, 30 | eqeq12d 2185 |
. . . . . . . 8
|
34 | 28, 33 | bibi12d 234 |
. . . . . . 7
|
35 | 34 | spc2gv 2821 |
. . . . . 6
|
36 | 26, 27, 35 | mp2an 424 |
. . . . 5
|
37 | | 0ex 4114 |
. . . . . . . 8
|
38 | 37 | snid 3612 |
. . . . . . 7
|
39 | | eleq2 2234 |
. . . . . . 7
|
40 | 38, 39 | mpbiri 167 |
. . . . . 6
|
41 | | eldifn 3250 |
. . . . . . . 8
|
42 | 41 | orim2i 756 |
. . . . . . 7
|
43 | | elun 3268 |
. . . . . . 7
|
44 | | df-dc 830 |
. . . . . . 7
DECID |
45 | 42, 43, 44 | 3imtr4i 200 |
. . . . . 6
DECID |
46 | 40, 45 | syl 14 |
. . . . 5
DECID |
47 | 36, 46 | syl6bi 162 |
. . . 4
DECID |
48 | 47 | alrimiv 1867 |
. . 3
DECID |
49 | | df-exmid 4179 |
. . 3
EXMID
DECID |
50 | 48, 49 | sylibr 133 |
. 2
EXMID |
51 | 25, 50 | impbii 125 |
1
EXMID
|