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Theorem biadan2OLD 26436
Description: Add a conjunction to an equivalence. (Moved to biadan2 623 in main set.mm and may be deleted by mathbox owner, JM. --NM 25-Feb-2014.) (Contributed by Jeff Madsen, 20-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
biadan2OLD.1  |-  ( ph  ->  ps )
biadan2OLD.2  |-  ( ps 
->  ( ph  <->  ch )
)
Assertion
Ref Expression
biadan2OLD  |-  ( ph  <->  ( ps  /\  ch )
)

Proof of Theorem biadan2OLD
StepHypRef Expression
1 biadan2OLD.1 . 2  |-  ( ph  ->  ps )
2 biadan2OLD.2 . 2  |-  ( ps 
->  ( ph  <->  ch )
)
31, 2biadan2 623 1  |-  ( ph  <->  ( ps  /\  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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