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Theorem mpbidi 219
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 210 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
41, 3sylcom 30 1  |-  ( th 
->  ( ph  ->  ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188
This theorem is referenced by:  tpid3g  4118  ralxfr2d  4638  ovmpt4g  6433  ov3  6447  omeulem2  7292  domtriomlem  8870  nsmallnq  9401  bposlem1  24075  pntrsumbnd  24267  mptsnunlem  31474  poimirlem27  31674  frege92  36191  nzss  36306
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