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Mirrors > Home > ILE Home > Th. List > ifeq1 | Unicode version |
Description: Equality theorem for conditional operator. (Contributed by NM, 1-Sep-2004.) (Revised by Mario Carneiro, 8-Sep-2013.) |
Ref | Expression |
---|---|
ifeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabeq 2595 | . . 3 | |
2 | 1 | uneq1d 3125 | . 2 |
3 | dfif6 3353 | . 2 | |
4 | dfif6 3353 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1284 crab 2352 cun 2971 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-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: ifeq12 3365 ifeq1d 3366 ifbieq12i 3374 |
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