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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 2299 | . 2 | |
2 | nfcv 2299 | . 2 | |
3 | 1, 2 | rexcomf 2619 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wrex 2436 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 |
This theorem is referenced by: rexcom13 2622 rexcom4 2735 iuncom 3857 xpiundi 4646 addcomprg 7500 mulcomprg 7502 ltexprlemm 7522 caucvgprprlemexbt 7628 suplocexprlemml 7638 suplocexprlemmu 7640 qmulz 9538 elpq 9563 caubnd2 11028 sqrt2irr 12052 pythagtriplem19 12172 |
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