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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 2727 | . . 3 | |
2 | 1 | uneq1d 3286 | . 2 |
3 | dfif6 3534 | . 2 | |
4 | dfif6 3534 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2233 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1353 crab 2457 cun 3125 cif 3532 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-ext 2157 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1459 df-sb 1761 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-rab 2462 df-v 2737 df-un 3131 df-if 3533 |
This theorem is referenced by: ifeq12 3548 ifeq1d 3549 ifbieq12i 3557 cbvsum 11335 prodeq2w 11531 cbvprod 11533 zproddc 11554 |
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