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Theorem ifeq2daOLD 26481
Description: Conditional equality. (Contributed by Jeff Madsen, 2-Sep-2009.) (Moved to ifeq2da 3604 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 3604 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 1632   ifcif 3578
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-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-un 3170  df-if 3579
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