Proof of Theorem wsuclemOLD
Step | Hyp | Ref
| Expression |
1 | | wsuclem.1 |
. . 3
|
2 | | wsuclem.2 |
. . 3
Se |
3 | | predss 5687 |
. . . 4
|
4 | 3 | a1i 11 |
. . 3
|
5 | | wsuclem.3 |
. . . . 5
|
6 | | dfpred3g 5691 |
. . . . 5
|
7 | 5, 6 | syl 17 |
. . . 4
|
8 | | elex 3212 |
. . . . . 6
|
9 | 5, 8 | syl 17 |
. . . . 5
|
10 | | wsuclem.4 |
. . . . 5
|
11 | | rabn0 3958 |
. . . . . . 7
|
12 | | brcnvg 5303 |
. . . . . . . . 9
|
13 | 12 | ancoms 469 |
. . . . . . . 8
|
14 | 13 | rexbidva 3049 |
. . . . . . 7
|
15 | 11, 14 | syl5bb 272 |
. . . . . 6
|
16 | 15 | biimpar 502 |
. . . . 5
|
17 | 9, 10, 16 | syl2anc 693 |
. . . 4
|
18 | 7, 17 | eqnetrd 2861 |
. . 3
|
19 | | tz6.26 5711 |
. . 3
Se
|
20 | 1, 2, 4, 18, 19 | syl22anc 1327 |
. 2
|
21 | | dfpred3g 5691 |
. . . . 5
|
22 | 5, 21 | syl 17 |
. . . 4
|
23 | 22 | rexeqdv 3145 |
. . 3
|
24 | | breq1 4656 |
. . . . 5
|
25 | 24 | rexrab 3370 |
. . . 4
|
26 | | noel 3919 |
. . . . . . . . . . . . 13
|
27 | | simp2r 1088 |
. . . . . . . . . . . . . 14
|
28 | 27 | eleq2d 2687 |
. . . . . . . . . . . . 13
|
29 | 26, 28 | mtbiri 317 |
. . . . . . . . . . . 12
|
30 | | vex 3203 |
. . . . . . . . . . . . . 14
|
31 | 30 | a1i 11 |
. . . . . . . . . . . . 13
|
32 | | simp3 1063 |
. . . . . . . . . . . . 13
|
33 | | elpredg 5694 |
. . . . . . . . . . . . 13
|
34 | 31, 32, 33 | syl2anc 693 |
. . . . . . . . . . . 12
|
35 | 29, 34 | mtbid 314 |
. . . . . . . . . . 11
|
36 | | vex 3203 |
. . . . . . . . . . . 12
|
37 | 30, 36 | brcnv 5305 |
. . . . . . . . . . 11
|
38 | 35, 37 | sylnibr 319 |
. . . . . . . . . 10
|
39 | 38 | 3expa 1265 |
. . . . . . . . 9
|
40 | 39 | ralrimiva 2966 |
. . . . . . . 8
|
41 | 40 | expr 643 |
. . . . . . 7
|
42 | | simp1rl 1126 |
. . . . . . . . . . . 12
|
43 | | simp1rr 1127 |
. . . . . . . . . . . 12
|
44 | | simp1l 1085 |
. . . . . . . . . . . . . 14
|
45 | 44, 5 | syl 17 |
. . . . . . . . . . . . 13
|
46 | 30 | elpred 5693 |
. . . . . . . . . . . . 13
|
47 | 45, 46 | syl 17 |
. . . . . . . . . . . 12
|
48 | 42, 43, 47 | mpbir2and 957 |
. . . . . . . . . . 11
|
49 | | simp3 1063 |
. . . . . . . . . . 11
|
50 | | breq2 4657 |
. . . . . . . . . . . 12
|
51 | 50 | rspcev 3309 |
. . . . . . . . . . 11
|
52 | 48, 49, 51 | syl2anc 693 |
. . . . . . . . . 10
|
53 | 52 | 3expia 1267 |
. . . . . . . . 9
|
54 | 53 | ralrimiva 2966 |
. . . . . . . 8
|
55 | 54 | expr 643 |
. . . . . . 7
|
56 | 41, 55 | anim12d 586 |
. . . . . 6
|
57 | 56 | ancomsd 470 |
. . . . 5
|
58 | 57 | reximdva 3017 |
. . . 4
|
59 | 25, 58 | syl5bi 232 |
. . 3
|
60 | 23, 59 | sylbid 230 |
. 2
|
61 | 20, 60 | mpd 15 |
1
|