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Mirrors > Home > ILE Home > Th. List > ralxpf | Unicode version |
Description: Version of ralxp 4682 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 2668 | . 2 | |
2 | cbvralsv 2668 | . . . 4 | |
3 | 2 | ralbii 2441 | . . 3 |
4 | nfv 1508 | . . . 4 | |
5 | nfcv 2281 | . . . . 5 | |
6 | nfs1v 1912 | . . . . 5 | |
7 | 5, 6 | nfralxy 2471 | . . . 4 |
8 | sbequ12 1744 | . . . . 5 | |
9 | 8 | ralbidv 2437 | . . . 4 |
10 | 4, 7, 9 | cbvral 2650 | . . 3 |
11 | vex 2689 | . . . . . 6 | |
12 | vex 2689 | . . . . . 6 | |
13 | 11, 12 | eqvinop 4165 | . . . . 5 |
14 | ralxpf.1 | . . . . . . . 8 | |
15 | 14 | nfsb 1919 | . . . . . . 7 |
16 | 6 | nfsb 1919 | . . . . . . 7 |
17 | 15, 16 | nfbi 1568 | . . . . . 6 |
18 | ralxpf.2 | . . . . . . . . 9 | |
19 | 18 | nfsb 1919 | . . . . . . . 8 |
20 | nfs1v 1912 | . . . . . . . 8 | |
21 | 19, 20 | nfbi 1568 | . . . . . . 7 |
22 | ralxpf.3 | . . . . . . . . 9 | |
23 | ralxpf.4 | . . . . . . . . 9 | |
24 | 22, 23 | sbhypf 2735 | . . . . . . . 8 |
25 | vex 2689 | . . . . . . . . . 10 | |
26 | vex 2689 | . . . . . . . . . 10 | |
27 | 25, 26 | opth 4159 | . . . . . . . . 9 |
28 | sbequ12 1744 | . . . . . . . . . 10 | |
29 | 8, 28 | sylan9bb 457 | . . . . . . . . 9 |
30 | 27, 29 | sylbi 120 | . . . . . . . 8 |
31 | 24, 30 | sylan9bb 457 | . . . . . . 7 |
32 | 21, 31 | exlimi 1573 | . . . . . 6 |
33 | 17, 32 | exlimi 1573 | . . . . 5 |
34 | 13, 33 | sylbi 120 | . . . 4 |
35 | 34 | ralxp 4682 | . . 3 |
36 | 3, 10, 35 | 3bitr4ri 212 | . 2 |
37 | 1, 36 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wnf 1436 wex 1468 wsb 1735 wral 2416 cop 3530 cxp 4537 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-iun 3815 df-opab 3990 df-xp 4545 df-rel 4546 |
This theorem is referenced by: (None) |
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