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Mirrors > Home > ILE Home > Th. List > ralxpf | Unicode version |
Description: Version of ralxp 4732 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 2694 | . 2 | |
2 | cbvralsv 2694 | . . . 4 | |
3 | 2 | ralbii 2463 | . . 3 |
4 | nfv 1508 | . . . 4 | |
5 | nfcv 2299 | . . . . 5 | |
6 | nfs1v 1919 | . . . . 5 | |
7 | 5, 6 | nfralxy 2495 | . . . 4 |
8 | sbequ12 1751 | . . . . 5 | |
9 | 8 | ralbidv 2457 | . . . 4 |
10 | 4, 7, 9 | cbvral 2676 | . . 3 |
11 | vex 2715 | . . . . . 6 | |
12 | vex 2715 | . . . . . 6 | |
13 | 11, 12 | eqvinop 4206 | . . . . 5 |
14 | ralxpf.1 | . . . . . . . 8 | |
15 | 14 | nfsb 1926 | . . . . . . 7 |
16 | 6 | nfsb 1926 | . . . . . . 7 |
17 | 15, 16 | nfbi 1569 | . . . . . 6 |
18 | ralxpf.2 | . . . . . . . . 9 | |
19 | 18 | nfsb 1926 | . . . . . . . 8 |
20 | nfs1v 1919 | . . . . . . . 8 | |
21 | 19, 20 | nfbi 1569 | . . . . . . 7 |
22 | ralxpf.3 | . . . . . . . . 9 | |
23 | ralxpf.4 | . . . . . . . . 9 | |
24 | 22, 23 | sbhypf 2761 | . . . . . . . 8 |
25 | vex 2715 | . . . . . . . . . 10 | |
26 | vex 2715 | . . . . . . . . . 10 | |
27 | 25, 26 | opth 4200 | . . . . . . . . 9 |
28 | sbequ12 1751 | . . . . . . . . . 10 | |
29 | 8, 28 | sylan9bb 458 | . . . . . . . . 9 |
30 | 27, 29 | sylbi 120 | . . . . . . . 8 |
31 | 24, 30 | sylan9bb 458 | . . . . . . 7 |
32 | 21, 31 | exlimi 1574 | . . . . . 6 |
33 | 17, 32 | exlimi 1574 | . . . . 5 |
34 | 13, 33 | sylbi 120 | . . . 4 |
35 | 34 | ralxp 4732 | . . 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 1335 wnf 1440 wex 1472 wsb 1742 wral 2435 cop 3564 cxp 4587 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4085 ax-pow 4138 ax-pr 4172 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-iun 3853 df-opab 4029 df-xp 4595 df-rel 4596 |
This theorem is referenced by: (None) |
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