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Mirrors > Home > ILE Home > Th. List > ralxpf | Unicode version |
Description: Version of ralxp 4497 with bound-variable hypotheses. (Contributed by NM, 18-Aug-2006.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
ralxpf.1 | |
ralxpf.2 | |
ralxpf.3 | |
ralxpf.4 |
Ref | Expression |
---|---|
ralxpf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralsv 2588 | . 2 | |
2 | cbvralsv 2588 | . . . 4 | |
3 | 2 | ralbii 2372 | . . 3 |
4 | nfv 1461 | . . . 4 | |
5 | nfcv 2219 | . . . . 5 | |
6 | nfs1v 1856 | . . . . 5 | |
7 | 5, 6 | nfralxy 2402 | . . . 4 |
8 | sbequ12 1694 | . . . . 5 | |
9 | 8 | ralbidv 2368 | . . . 4 |
10 | 4, 7, 9 | cbvral 2573 | . . 3 |
11 | vex 2604 | . . . . . 6 | |
12 | vex 2604 | . . . . . 6 | |
13 | 11, 12 | eqvinop 3998 | . . . . 5 |
14 | ralxpf.1 | . . . . . . . 8 | |
15 | 14 | nfsb 1863 | . . . . . . 7 |
16 | 6 | nfsb 1863 | . . . . . . 7 |
17 | 15, 16 | nfbi 1521 | . . . . . 6 |
18 | ralxpf.2 | . . . . . . . . 9 | |
19 | 18 | nfsb 1863 | . . . . . . . 8 |
20 | nfs1v 1856 | . . . . . . . 8 | |
21 | 19, 20 | nfbi 1521 | . . . . . . 7 |
22 | ralxpf.3 | . . . . . . . . 9 | |
23 | ralxpf.4 | . . . . . . . . 9 | |
24 | 22, 23 | sbhypf 2648 | . . . . . . . 8 |
25 | vex 2604 | . . . . . . . . . 10 | |
26 | vex 2604 | . . . . . . . . . 10 | |
27 | 25, 26 | opth 3992 | . . . . . . . . 9 |
28 | sbequ12 1694 | . . . . . . . . . 10 | |
29 | 8, 28 | sylan9bb 449 | . . . . . . . . 9 |
30 | 27, 29 | sylbi 119 | . . . . . . . 8 |
31 | 24, 30 | sylan9bb 449 | . . . . . . 7 |
32 | 21, 31 | exlimi 1525 | . . . . . 6 |
33 | 17, 32 | exlimi 1525 | . . . . 5 |
34 | 13, 33 | sylbi 119 | . . . 4 |
35 | 34 | ralxp 4497 | . . 3 |
36 | 3, 10, 35 | 3bitr4ri 211 | . 2 |
37 | 1, 36 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wex 1421 wsb 1685 wral 2348 cop 3401 cxp 4361 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-sbc 2816 df-csb 2909 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-iun 3680 df-opab 3840 df-xp 4369 df-rel 4370 |
This theorem is referenced by: (None) |
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