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Mirrors > Home > ILE Home > Th. List > ralxpf | Unicode version |
Description: Version of ralxp 4754 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 2712 | . 2 | |
2 | cbvralsv 2712 | . . . 4 | |
3 | 2 | ralbii 2476 | . . 3 |
4 | nfv 1521 | . . . 4 | |
5 | nfcv 2312 | . . . . 5 | |
6 | nfs1v 1932 | . . . . 5 | |
7 | 5, 6 | nfralxy 2508 | . . . 4 |
8 | sbequ12 1764 | . . . . 5 | |
9 | 8 | ralbidv 2470 | . . . 4 |
10 | 4, 7, 9 | cbvral 2692 | . . 3 |
11 | vex 2733 | . . . . . 6 | |
12 | vex 2733 | . . . . . 6 | |
13 | 11, 12 | eqvinop 4228 | . . . . 5 |
14 | ralxpf.1 | . . . . . . . 8 | |
15 | 14 | nfsb 1939 | . . . . . . 7 |
16 | 6 | nfsb 1939 | . . . . . . 7 |
17 | 15, 16 | nfbi 1582 | . . . . . 6 |
18 | ralxpf.2 | . . . . . . . . 9 | |
19 | 18 | nfsb 1939 | . . . . . . . 8 |
20 | nfs1v 1932 | . . . . . . . 8 | |
21 | 19, 20 | nfbi 1582 | . . . . . . 7 |
22 | ralxpf.3 | . . . . . . . . 9 | |
23 | ralxpf.4 | . . . . . . . . 9 | |
24 | 22, 23 | sbhypf 2779 | . . . . . . . 8 |
25 | vex 2733 | . . . . . . . . . 10 | |
26 | vex 2733 | . . . . . . . . . 10 | |
27 | 25, 26 | opth 4222 | . . . . . . . . 9 |
28 | sbequ12 1764 | . . . . . . . . . 10 | |
29 | 8, 28 | sylan9bb 459 | . . . . . . . . 9 |
30 | 27, 29 | sylbi 120 | . . . . . . . 8 |
31 | 24, 30 | sylan9bb 459 | . . . . . . 7 |
32 | 21, 31 | exlimi 1587 | . . . . . 6 |
33 | 17, 32 | exlimi 1587 | . . . . 5 |
34 | 13, 33 | sylbi 120 | . . . 4 |
35 | 34 | ralxp 4754 | . . 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 1348 wnf 1453 wex 1485 wsb 1755 wral 2448 cop 3586 cxp 4609 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-iun 3875 df-opab 4051 df-xp 4617 df-rel 4618 |
This theorem is referenced by: (None) |
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