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Mirrors > Home > ILE Home > Th. List > ifbieq2d | Unicode version |
Description: Equivalence/equality deduction for conditional operators. (Contributed by Paul Chapman, 22-Jun-2011.) |
Ref | Expression |
---|---|
ifbieq2d.1 | |
ifbieq2d.2 |
Ref | Expression |
---|---|
ifbieq2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifbieq2d.1 | . . 3 | |
2 | 1 | ifbid 3370 | . 2 |
3 | ifbieq2d.2 | . . 3 | |
4 | 3 | ifeq2d 3367 | . 2 |
5 | 2, 4 | eqtrd 2113 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wceq 1284 cif 3351 |
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-in1 576 ax-in2 577 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-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rab 2357 df-v 2603 df-un 2977 df-if 3352 |
This theorem is referenced by: xnegeq 8894 expival 9478 gcdval 10351 gcdass 10404 lcmval 10445 lcmass 10467 |
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