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Mirrors > Home > MPE Home > Th. List > iffalsei | Structured version Visualization version GIF version |
Description: Inference associated with iffalse 4474. (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 4474 | . 2 ⊢ (¬ 𝜑 → if(𝜑, 𝐴, 𝐵) = 𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ if(𝜑, 𝐴, 𝐵) = 𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 = wceq 1528 ifcif 4465 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-ext 2793 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-ex 1772 df-sb 2061 df-clab 2800 df-cleq 2814 df-clel 2893 df-if 4466 |
This theorem is referenced by: sum0 15068 prod0 15287 prmo4 16451 prmo6 16453 itg0 24309 vieta1lem2 24829 vtxval0 26752 iedgval0 26753 ex-prmo 28166 dfrdg2 32938 dfrdg4 33310 fwddifnp1 33524 bj-pr21val 34223 bj-pr22val 34229 clsk1indlem4 40274 clsk1indlem1 40275 refsum2cnlem1 41174 limsup10ex 41934 iblempty 42130 fouriersw 42397 |
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