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Mirrors > Home > ILE Home > Th. List > rexcom | Unicode version |
Description: Commutation of restricted quantifiers. (Contributed by NM, 19-Nov-1995.) (Revised by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
rexcom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2312 | . 2 | |
2 | nfcv 2312 | . 2 | |
3 | 1, 2 | rexcomf 2632 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wrex 2449 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 |
This theorem is referenced by: rexcom13 2635 rexcom4 2753 iuncom 3879 xpiundi 4669 addcomprg 7540 mulcomprg 7542 ltexprlemm 7562 caucvgprprlemexbt 7668 suplocexprlemml 7678 suplocexprlemmu 7680 qmulz 9582 elpq 9607 caubnd2 11081 sqrt2irr 12116 pythagtriplem19 12236 |
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