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Theorem mpbirand 438
Description: Detach truth from conjunction in biconditional. (Contributed by Glauco Siliprandi, 3-Mar-2021.)
Hypotheses
Ref Expression
mpbirand.1  |-  ( ph  ->  ch )
mpbirand.2  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
Assertion
Ref Expression
mpbirand  |-  ( ph  ->  ( ps  <->  th )
)

Proof of Theorem mpbirand
StepHypRef Expression
1 mpbirand.2 . 2  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
2 mpbirand.1 . . 3  |-  ( ph  ->  ch )
32biantrurd 303 . 2  |-  ( ph  ->  ( th  <->  ( ch  /\ 
th ) ) )
41, 3bitr4d 190 1  |-  ( ph  ->  ( ps  <->  th )
)
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:  fprodssdc  11487  txmetcn  12930
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