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Mirrors > Home > ILE Home > Th. List > rexcom4 | Unicode version |
Description: Commutation of restricted and unrestricted existential quantifiers. (Contributed by NM, 12-Apr-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
rexcom4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexcom 2569 |
. 2
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2 | rexv 2675 |
. . 3
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3 | 2 | rexbii 2416 |
. 2
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4 | rexv 2675 |
. 2
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5 | 1, 3, 4 | 3bitr3i 209 |
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 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-rex 2396 df-v 2659 |
This theorem is referenced by: rexcom4a 2681 reuind 2858 iuncom4 3786 dfiun2g 3811 iunn0m 3839 iunxiun 3860 iinexgm 4039 inuni 4040 iunopab 4163 xpiundi 4557 xpiundir 4558 cnvuni 4685 dmiun 4708 elres 4813 elsnres 4814 rniun 4907 imaco 5002 coiun 5006 fun11iun 5344 abrexco 5614 imaiun 5615 fliftf 5654 rexrnmpo 5840 oprabrexex2 5982 releldm2 6037 eroveu 6474 genpassl 7280 genpassu 7281 ltexprlemopl 7357 ltexprlemopu 7359 ntreq0 12144 metrest 12495 |
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