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Theorem iffv 6924
Description: Move a conditional outside of a function. (Contributed by Thierry Arnoux, 28-Sep-2018.)
Assertion
Ref Expression
iffv (if(𝜑, 𝐹, 𝐺)‘𝐴) = if(𝜑, (𝐹𝐴), (𝐺𝐴))

Proof of Theorem iffv
StepHypRef Expression
1 fveq1 6906 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐹 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐹𝐴))
2 fveq1 6906 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐺 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐺𝐴))
31, 2ifsb 4544 1 (if(𝜑, 𝐹, 𝐺)‘𝐴) = if(𝜑, (𝐹𝐴), (𝐺𝐴))
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  ifcif 4531  cfv 6563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-if 4532  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571
This theorem is referenced by:  decpmatid  22792  pmatcollpwscmatlem1  22811  selvvvval  42572  prjspnfv01  42611
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