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Theorem mpbidi 149
Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994.)
Hypotheses
Ref Expression
mpbidi.min  |-  ( th 
->  ( ph  ->  ps ) )
mpbidi.maj  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
mpbidi  |-  ( th 
->  ( ph  ->  ch ) )

Proof of Theorem mpbidi
StepHypRef Expression
1 mpbidi.min . 2  |-  ( th 
->  ( ph  ->  ps ) )
2 mpbidi.maj . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
32biimpd 142 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
41, 3sylcom 28 1  |-  ( th 
->  ( ph  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  tpid3g  3513  ralxfr2d  4222  rexxfr2d  4223  ovmpt4g  5654  ovi3  5668  bj-inf2vnlem1  10923
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