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Theorem ibd 243
Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 26-Jun-2004.)
Hypothesis
Ref Expression
ibd.1  |-  ( ph  ->  ( ps  ->  ( ps 
<->  ch ) ) )
Assertion
Ref Expression
ibd  |-  ( ph  ->  ( ps  ->  ch ) )

Proof of Theorem ibd
StepHypRef Expression
1 ibd.1 . 2  |-  ( ph  ->  ( ps  ->  ( ps 
<->  ch ) ) )
2 bi1 186 . 2  |-  ( ( ps  <->  ch )  ->  ( ps  ->  ch ) )
31, 2syli 37 1  |-  ( ph  ->  ( ps  ->  ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185
This theorem is referenced by:  sssn  4140  unblem2  7677  atcv0eq  25936  atcv1  25937  atomli  25939  atcvatlem  25942  ibdr  29146
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