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Theorem iffv 6518
 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 6500 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐹 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐹𝐴))
2 fveq1 6500 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐺 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐺𝐴))
31, 2ifsb 4364 1 (if(𝜑, 𝐹, 𝐺)‘𝐴) = if(𝜑, (𝐹𝐴), (𝐺𝐴))
 Colors of variables: wff setvar class Syntax hints:   = wceq 1507  ifcif 4351  ‘cfv 6190 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-ext 2750 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-ex 1743  df-sb 2016  df-clab 2759  df-cleq 2771  df-clel 2846  df-rex 3094  df-if 4352  df-uni 4714  df-br 4931  df-iota 6154  df-fv 6198 This theorem is referenced by:  decpmatid  21085  pmatcollpwscmatlem1  21104
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