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Mirrors > Home > ILE Home > Th. List > ifbieq12d | Unicode version |
Description: Equivalence deduction for conditional operators. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
ifbieq12d.1 | |
ifbieq12d.2 | |
ifbieq12d.3 |
Ref | Expression |
---|---|
ifbieq12d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifbieq12d.1 | . . 3 | |
2 | 1 | ifbid 3546 | . 2 |
3 | ifbieq12d.2 | . . 3 | |
4 | ifbieq12d.3 | . . 3 | |
5 | 3, 4 | ifeq12d 3544 | . 2 |
6 | 2, 5 | eqtrd 2203 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1348 cif 3525 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rab 2457 df-v 2732 df-un 3125 df-if 3526 |
This theorem is referenced by: updjudhcoinlf 7055 updjudhcoinrg 7056 omp1eom 7070 xaddval 9795 iseqf1olemqval 10436 iseqf1olemqk 10443 seq3f1olemqsum 10449 exp3val 10471 cvgratz 11488 eucalgval2 12000 ennnfonelemg 12351 ennnfonelem1 12355 ressid2 12470 ressval2 12471 lgsval 13664 |
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