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Mirrors > Home > ILE Home > Th. List > iffalsei | GIF version |
Description: Inference associated with iffalse 3561. (Contributed by BJ, 7-Oct-2018.) |
Ref | Expression |
---|---|
iffalsei.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
iffalsei | ⊢ if(𝜑, 𝐴, 𝐵) = 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iffalsei.1 | . 2 ⊢ ¬ 𝜑 | |
2 | iffalse 3561 | . 2 ⊢ (¬ 𝜑 → if(𝜑, 𝐴, 𝐵) = 𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ if(𝜑, 𝐴, 𝐵) = 𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1364 ifcif 3553 |
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-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-if 3554 |
This theorem is referenced by: 0tonninf 10497 sum0 11505 prod0 11702 ennnfonelem1 12538 dcapnconst 15475 |
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