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Mirrors > Home > ILE Home > Th. List > rexxp | Unicode version |
Description: Existential quantification restricted to a cross product is equivalent to a double restricted quantification. (Contributed by NM, 11-Nov-1995.) (Revised by Mario Carneiro, 14-Feb-2015.) |
Ref | Expression |
---|---|
ralxp.1 |
Ref | Expression |
---|---|
rexxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunxpconst 4646 | . . 3 | |
2 | 1 | rexeqi 2657 | . 2 |
3 | ralxp.1 | . . 3 | |
4 | 3 | rexiunxp 4728 | . 2 |
5 | 2, 4 | bitr3i 185 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1335 wrex 2436 csn 3560 cop 3563 ciun 3849 cxp 4584 |
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 4082 ax-pow 4135 ax-pr 4169 |
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 3545 df-sn 3566 df-pr 3567 df-op 3569 df-iun 3851 df-opab 4026 df-xp 4592 df-rel 4593 |
This theorem is referenced by: rexxpf 4733 fnrnov 5966 foov 5967 ovelimab 5971 xpf1o 6789 cnref1o 9559 txbas 12669 |
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