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Theorem ifeq2daOLD 26378
Description: Conditional equality. (Contributed by Jeff Madsen, 2-Sep-2009.) (Moved to ifeq2da 3591 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
ifeq2daOLD.1  |-  ( (
ph  /\  -.  ps )  ->  A  =  B )
Assertion
Ref Expression
ifeq2daOLD  |-  ( ph  ->  if ( ps ,  C ,  A )  =  if ( ps ,  C ,  B )
)

Proof of Theorem ifeq2daOLD
StepHypRef Expression
1 ifeq2daOLD.1 . 2  |-  ( (
ph  /\  -.  ps )  ->  A  =  B )
21ifeq2da 3591 1  |-  ( ph  ->  if ( ps ,  C ,  A )  =  if ( ps ,  C ,  B )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358    = wceq 1623   ifcif 3565
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-un 3157  df-if 3566
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