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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexcom 2518 | . 2 | |
2 | rexv 2617 | . . 3 | |
3 | 2 | rexbii 2373 | . 2 |
4 | rexv 2617 | . 2 | |
5 | 1, 3, 4 | 3bitr3i 208 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 103 wex 1421 wrex 2349 cvv 2601 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 |
This theorem is referenced by: rexcom4a 2623 reuind 2795 iuncom4 3685 dfiun2g 3710 iunn0m 3738 iunxiun 3757 iinexgm 3929 inuni 3930 iunopab 4036 xpiundi 4416 xpiundir 4417 cnvuni 4539 dmiun 4562 elres 4664 elsnres 4665 rniun 4754 imaco 4846 coiun 4850 fun11iun 5167 abrexco 5419 imaiun 5420 fliftf 5459 rexrnmpt2 5636 oprabrexex2 5777 releldm2 5831 eroveu 6220 genpassl 6714 genpassu 6715 ltexprlemopl 6791 ltexprlemopu 6793 |
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