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Theorem iffv 6913
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 6895 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐹 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐹𝐴))
2 fveq1 6895 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐺 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐺𝐴))
31, 2ifsb 4543 1 (if(𝜑, 𝐹, 𝐺)‘𝐴) = if(𝜑, (𝐹𝐴), (𝐺𝐴))
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  ifcif 4530  cfv 6549
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463  df-ss 3961  df-if 4531  df-uni 4910  df-br 5150  df-iota 6501  df-fv 6557
This theorem is referenced by:  decpmatid  22716  pmatcollpwscmatlem1  22735  selvvvval  41953  prjspnfv01  42183
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