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Mirrors > Home > ILE Home > Th. List > raltp | Unicode version |
Description: Convert a quantification over a triple to a conjunction. (Contributed by NM, 13-Sep-2011.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
raltp.1 | |
raltp.2 | |
raltp.3 | |
raltp.4 | |
raltp.5 | |
raltp.6 |
Ref | Expression |
---|---|
raltp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raltp.1 | . 2 | |
2 | raltp.2 | . 2 | |
3 | raltp.3 | . 2 | |
4 | raltp.4 | . . 3 | |
5 | raltp.5 | . . 3 | |
6 | raltp.6 | . . 3 | |
7 | 4, 5, 6 | raltpg 3576 | . 2 |
8 | 1, 2, 3, 7 | mp3an 1315 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 962 wceq 1331 wcel 1480 wral 2416 cvv 2686 ctp 3529 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
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-v 2688 df-sbc 2910 df-un 3075 df-sn 3533 df-pr 3534 df-tp 3535 |
This theorem is referenced by: fztpval 9863 |
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