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Theorem pm4.71d 388
Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by Mario Carneiro, 25-Dec-2016.)
Hypothesis
Ref Expression
pm4.71rd.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
pm4.71d  |-  ( ph  ->  ( ps  <->  ( ps  /\ 
ch ) ) )

Proof of Theorem pm4.71d
StepHypRef Expression
1 pm4.71rd.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 pm4.71 384 . 2  |-  ( ( ps  ->  ch )  <->  ( ps  <->  ( ps  /\  ch ) ) )
31, 2sylib 121 1  |-  ( ph  ->  ( ps  <->  ( ps  /\ 
ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  difin2  3306  resopab2  4834  fcnvres  5274  resoprab2  5834  cndis  12316  cnpdis  12317  blpnf  12475
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