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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 4685 |
. . 3
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2 | 1 | raleqi 2676 |
. 2
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3 | ralxp.1 |
. . 3
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4 | 3 | raliunxp 4766 |
. 2
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5 | 2, 4 | bitr3i 186 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-csb 3058 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-iun 3888 df-opab 4064 df-xp 4631 df-rel 4632 |
This theorem is referenced by: ralxpf 4771 issref 5009 ffnov 5975 eqfnov 5977 funimassov 6020 f1stres 6156 f2ndres 6157 ecopover 6629 ecopoverg 6632 xpf1o 6840 srgfcl 13078 txbas 13620 cnmpt21 13653 txmetcnp 13880 txmetcn 13881 qtopbasss 13883 |
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