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Theorem ifeq1daOLD 25884
Description: Conditional equality. (Contributed by Jeff Madsen, 2-Sep-2009.) (Moved to ifeq1da 3679 in main set.mm and may be deleted by mathbox owner, JM. --NM 16-Jan-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ifeq1daOLD.1  |-  ( (
ph  /\  ps )  ->  A  =  B )
Assertion
Ref Expression
ifeq1daOLD  |-  ( ph  ->  if ( ps ,  A ,  C )  =  if ( ps ,  B ,  C )
)

Proof of Theorem ifeq1daOLD
StepHypRef Expression
1 ifeq1daOLD.1 . 2  |-  ( (
ph  /\  ps )  ->  A  =  B )
21ifeq1da 3679 1  |-  ( ph  ->  if ( ps ,  A ,  C )  =  if ( ps ,  B ,  C )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1647   ifcif 3654
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-rab 2637  df-v 2875  df-un 3243  df-if 3655
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