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Theorem iffv 6773
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 6755 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐹 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐹𝐴))
2 fveq1 6755 . 2 (if(𝜑, 𝐹, 𝐺) = 𝐺 → (if(𝜑, 𝐹, 𝐺)‘𝐴) = (𝐺𝐴))
31, 2ifsb 4469 1 (if(𝜑, 𝐹, 𝐺)‘𝐴) = if(𝜑, (𝐹𝐴), (𝐺𝐴))
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  ifcif 4456  cfv 6418
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-if 4457  df-uni 4837  df-br 5071  df-iota 6376  df-fv 6426
This theorem is referenced by:  decpmatid  21827  pmatcollpwscmatlem1  21846  prjspnfv01  40382
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