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Theorem pm5.32rd 446
Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 25-Dec-2004.)
Hypothesis
Ref Expression
pm5.32d.1  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
Assertion
Ref Expression
pm5.32rd  |-  ( ph  ->  ( ( ch  /\  ps )  <->  ( th  /\  ps ) ) )

Proof of Theorem pm5.32rd
StepHypRef Expression
1 pm5.32d.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
21pm5.32d 445 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  <->  ( ps  /\  th ) ) )
3 ancom 264 . 2  |-  ( ( ch  /\  ps )  <->  ( ps  /\  ch )
)
4 ancom 264 . 2  |-  ( ( th  /\  ps )  <->  ( ps  /\  th )
)
52, 3, 43bitr4g 222 1  |-  ( ph  ->  ( ( ch  /\  ps )  <->  ( th  /\  ps ) ) )
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:  anbi1d  460  pm5.71dc  945  1idprl  7405  1idpru  7406
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