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Mirrors > Home > ILE Home > Th. List > ifbieq1d | Unicode version |
Description: Equivalence/equality deduction for conditional operators. (Contributed by JJ, 25-Sep-2018.) |
Ref | Expression |
---|---|
ifbieq1d.1 | |
ifbieq1d.2 |
Ref | Expression |
---|---|
ifbieq1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifbieq1d.1 | . . 3 | |
2 | 1 | ifbid 3463 | . 2 |
3 | ifbieq1d.2 | . . 3 | |
4 | 3 | ifeq1d 3459 | . 2 |
5 | 2, 4 | eqtrd 2150 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 cif 3444 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rab 2402 df-v 2662 df-un 3045 df-if 3445 |
This theorem is referenced by: ctssdclemn0 6963 ctssdc 6966 enumctlemm 6967 iseqf1olemfvp 10225 seq3f1olemqsum 10228 seq3f1oleml 10231 seq3f1o 10232 bcval 10450 sumrbdclem 11100 summodclem3 11104 summodclem2a 11105 summodc 11107 zsumdc 11108 fsum3 11111 isumss 11115 isumss2 11117 fsum3cvg2 11118 fsum3ser 11121 fsumcl2lem 11122 fsumadd 11130 sumsnf 11133 fsummulc2 11172 isumlessdc 11220 |
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