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Mirrors > Home > ILE Home > Th. List > rexcomf | Unicode version |
Description: Commutation of restricted quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
ralcomf.1 | |
ralcomf.2 |
Ref | Expression |
---|---|
rexcomf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 262 | . . . . 5 | |
2 | 1 | anbi1i 445 | . . . 4 |
3 | 2 | 2exbii 1537 | . . 3 |
4 | excom 1594 | . . 3 | |
5 | 3, 4 | bitri 182 | . 2 |
6 | ralcomf.1 | . . 3 | |
7 | 6 | r2exf 2384 | . 2 |
8 | ralcomf.2 | . . 3 | |
9 | 8 | r2exf 2384 | . 2 |
10 | 5, 7, 9 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 wex 1421 wcel 1433 wnfc 2206 wrex 2349 |
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-nf 1390 df-sb 1686 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 |
This theorem is referenced by: rexcom 2518 |
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