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Mirrors > Home > ILE Home > Th. List > ralcomf | Unicode version |
Description: Commutation of restricted quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
ralcomf.1 | |
ralcomf.2 |
Ref | Expression |
---|---|
ralcomf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancomsimp 1416 | . . . 4 | |
2 | 1 | 2albii 1447 | . . 3 |
3 | alcom 1454 | . . 3 | |
4 | 2, 3 | bitri 183 | . 2 |
5 | ralcomf.1 | . . 3 | |
6 | 5 | r2alf 2450 | . 2 |
7 | ralcomf.2 | . . 3 | |
8 | 7 | r2alf 2450 | . 2 |
9 | 4, 6, 8 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wcel 1480 wnfc 2266 wral 2414 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 |
This theorem is referenced by: ralcom 2592 ssiinf 3857 |
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