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Theorem fvifOLD 26479
Description: Move a conditional outside of a function. (Contributed by Jeff Madsen, 2-Sep-2009.) (Moved to fvif 5556 in main set.mm and may be deleted by mathbox owner, JM. --NM 16-Jan-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
fvifOLD  |-  ( F `
 if ( ph ,  A ,  B ) )  =  if (
ph ,  ( F `
 A ) ,  ( F `  B
) )

Proof of Theorem fvifOLD
StepHypRef Expression
1 fvif 5556 1  |-  ( F `
 if ( ph ,  A ,  B ) )  =  if (
ph ,  ( F `
 A ) ,  ( F `  B
) )
Colors of variables: wff set class
Syntax hints:    = wceq 1632   ifcif 3578   ` cfv 5271
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279
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