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Mirrors > Home > ILE Home > Th. List > ralpr | Unicode version |
Description: Convert a quantification over a pair to a conjunction. (Contributed by NM, 3-Jun-2007.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralpr.1 | |
ralpr.2 | |
ralpr.3 | |
ralpr.4 |
Ref | Expression |
---|---|
ralpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralpr.1 | . 2 | |
2 | ralpr.2 | . 2 | |
3 | ralpr.3 | . . 3 | |
4 | ralpr.4 | . . 3 | |
5 | 3, 4 | ralprg 3634 | . 2 |
6 | 1, 2, 5 | mp2an 424 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 wral 2448 cvv 2730 cpr 3584 |
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-ext 2152 |
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-v 2732 df-sbc 2956 df-un 3125 df-sn 3589 df-pr 3590 |
This theorem is referenced by: fzprval 10038 |
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