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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 2531 |
. 2
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2 | rexv 2637 |
. . 3
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3 | 2 | rexbii 2385 |
. 2
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4 | rexv 2637 |
. 2
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5 | 1, 3, 4 | 3bitr3i 208 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rex 2365 df-v 2621 |
This theorem is referenced by: rexcom4a 2643 reuind 2820 iuncom4 3737 dfiun2g 3762 iunn0m 3790 iunxiun 3810 iinexgm 3990 inuni 3991 iunopab 4108 xpiundi 4496 xpiundir 4497 cnvuni 4622 dmiun 4645 elres 4748 elsnres 4749 rniun 4842 imaco 4936 coiun 4940 fun11iun 5274 abrexco 5538 imaiun 5539 fliftf 5578 rexrnmpt2 5760 oprabrexex2 5901 releldm2 5955 eroveu 6381 genpassl 7081 genpassu 7082 ltexprlemopl 7158 ltexprlemopu 7160 |
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