Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rexprg | Unicode version |
Description: Convert a quantification over a pair to a disjunction. (Contributed by NM, 17-Sep-2011.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralprg.1 | |
ralprg.2 |
Ref | Expression |
---|---|
rexprg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr 3405 | . . . 4 | |
2 | 1 | rexeqi 2554 | . . 3 |
3 | rexun 3152 | . . 3 | |
4 | 2, 3 | bitri 182 | . 2 |
5 | ralprg.1 | . . . . 5 | |
6 | 5 | rexsng 3434 | . . . 4 |
7 | 6 | orbi1d 737 | . . 3 |
8 | ralprg.2 | . . . . 5 | |
9 | 8 | rexsng 3434 | . . . 4 |
10 | 9 | orbi2d 736 | . . 3 |
11 | 7, 10 | sylan9bb 449 | . 2 |
12 | 4, 11 | syl5bb 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wo 661 wceq 1284 wcel 1433 wrex 2349 cun 2971 csn 3398 cpr 3399 |
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-3an 921 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 df-sbc 2816 df-un 2977 df-sn 3404 df-pr 3405 |
This theorem is referenced by: rextpg 3446 rexpr 3448 minmax 10112 |
Copyright terms: Public domain | W3C validator |