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Theorem iffv 6669
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 6651 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐹 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐹𝐴))
2 fveq1 6651 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐺 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐺𝐴))
31, 2ifsb 4452 1 (if(𝜑, 𝐹, 𝐺)‘𝐴) = if(𝜑, (𝐹𝐴), (𝐺𝐴))
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  ifcif 4439  cfv 6334
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-in 3915  df-ss 3925  df-if 4440  df-uni 4814  df-br 5043  df-iota 6293  df-fv 6342
This theorem is referenced by:  decpmatid  21373  pmatcollpwscmatlem1  21392
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