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Theorem mpbiran2d 436
Description: Detach truth from conjunction in biconditional. Deduction form. (Contributed by Peter Mazsa, 24-Sep-2022.)
Hypotheses
Ref Expression
mpbiran2d.1  |-  ( ph  ->  th )
mpbiran2d.2  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
Assertion
Ref Expression
mpbiran2d  |-  ( ph  ->  ( ps  <->  ch )
)

Proof of Theorem mpbiran2d
StepHypRef Expression
1 mpbiran2d.2 . 2  |-  ( ph  ->  ( ps  <->  ( ch  /\ 
th ) ) )
2 mpbiran2d.1 . . 3  |-  ( ph  ->  th )
32biantrud 300 . 2  |-  ( ph  ->  ( ch  <->  ( ch  /\ 
th ) ) )
41, 3bitr4d 190 1  |-  ( ph  ->  ( 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: (None)
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