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Mirrors > Home > ILE Home > Th. List > ifbieq2i | Unicode version |
Description: Equivalence/equality inference for conditional operators. (Contributed by Paul Chapman, 22-Jun-2011.) |
Ref | Expression |
---|---|
ifbieq2i.1 | |
ifbieq2i.2 |
Ref | Expression |
---|---|
ifbieq2i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifbieq2i.1 | . . 3 | |
2 | ifbi 3462 | . . 3 | |
3 | 1, 2 | ax-mp 5 | . 2 |
4 | ifbieq2i.2 | . . 3 | |
5 | ifeq2 3448 | . . 3 | |
6 | 4, 5 | ax-mp 5 | . 2 |
7 | 3, 6 | eqtri 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: 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: ifbieq12i 3467 gcdcom 11589 gcdass 11630 lcmcom 11672 lcmass 11693 |
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