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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 3629 | . 2 |
8 | 1, 2, 3, 7 | mp3an 1327 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 968 wceq 1343 wcel 2136 wral 2444 cvv 2726 ctp 3578 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ral 2449 df-v 2728 df-sbc 2952 df-un 3120 df-sn 3582 df-pr 3583 df-tp 3584 |
This theorem is referenced by: fztpval 10018 |
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