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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 |
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Ref | Expression |
---|---|
ralxp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunxpconst 4557 |
. . 3
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2 | 1 | raleqi 2602 |
. 2
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3 | ralxp.1 |
. . 3
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4 | 3 | raliunxp 4638 |
. 2
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5 | 2, 4 | bitr3i 185 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-sbc 2877 df-csb 2970 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-iun 3779 df-opab 3948 df-xp 4503 df-rel 4504 |
This theorem is referenced by: ralxpf 4643 issref 4877 ffnov 5827 eqfnov 5829 funimassov 5872 f1stres 6009 f2ndres 6010 ecopover 6479 ecopoverg 6482 xpf1o 6689 txbas 12263 cnmpt21 12296 txmetcnp 12501 txmetcn 12502 qtopbasss 12504 |
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