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Theorem ifcldaOLD 26482
Description: Conditional closure. (Contributed by Jeff Madsen, 2-Sep-2009.) (Moved to ifclda 3605 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 3605 1  |-  ( ph  ->  if ( ps ,  A ,  B )  e.  C )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358    e. wcel 1696   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-if 3579
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