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Theorem ifcldaOLD 26379
Description: Conditional closure. (Contributed by Jeff Madsen, 2-Sep-2009.) (Moved to ifclda 3592 in main set.mm and may be deleted by mathbox owner, JM. --NM 15-Jan-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ifcldaOLD.1  |-  ( (
ph  /\  ps )  ->  A  e.  C )
ifcldaOLD.2  |-  ( (
ph  /\  -.  ps )  ->  B  e.  C )
Assertion
Ref Expression
ifcldaOLD  |-  ( ph  ->  if ( ps ,  A ,  B )  e.  C )

Proof of Theorem ifcldaOLD
StepHypRef Expression
1 ifcldaOLD.1 . 2  |-  ( (
ph  /\  ps )  ->  A  e.  C )
2 ifcldaOLD.2 . 2  |-  ( (
ph  /\  -.  ps )  ->  B  e.  C )
31, 2ifclda 3592 1  |-  ( ph  ->  if ( ps ,  A ,  B )  e.  C )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358    e. wcel 1684   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-if 3566
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