ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpbidi Unicode version

Theorem mpbidi 150
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 143 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
41, 3sylcom 28 1  |-  ( th 
->  ( ph  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  tpid3g  3638  ralxfr2d  4385  rexxfr2d  4386  ovmpt4g  5893  ovi3  5907  bj-inf2vnlem1  13182
  Copyright terms: Public domain W3C validator