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Mirrors > Home > ILE Home > Th. List > ralxp | Unicode version |
Description: Universal quantification restricted to a cross product is equivalent to a double restricted quantification. The hypothesis specifies an implicit substitution. (Contributed by NM, 7-Feb-2004.) (Revised by Mario Carneiro, 29-Dec-2014.) |
Ref | Expression |
---|---|
ralxp.1 |
Ref | Expression |
---|---|
ralxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunxpconst 4569 | . . 3 | |
2 | 1 | raleqi 2607 | . 2 |
3 | ralxp.1 | . . 3 | |
4 | 3 | raliunxp 4650 | . 2 |
5 | 2, 4 | bitr3i 185 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 wral 2393 csn 3497 cop 3500 ciun 3783 cxp 4507 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-csb 2976 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-iun 3785 df-opab 3960 df-xp 4515 df-rel 4516 |
This theorem is referenced by: ralxpf 4655 issref 4891 ffnov 5843 eqfnov 5845 funimassov 5888 f1stres 6025 f2ndres 6026 ecopover 6495 ecopoverg 6498 xpf1o 6706 txbas 12354 cnmpt21 12387 txmetcnp 12614 txmetcn 12615 qtopbasss 12617 |
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