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Theorem mpbidi 216
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 207 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
41, 3sylcom 29 1  |-  ( th 
->  ( ph  ->  ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184
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 185
This theorem is referenced by:  tpid3g  4142  ralxfr2d  4663  ovmpt4g  6409  ov3  6423  omeulem2  7232  domtriomlem  8822  nsmallnq  9355  bposlem1  23315  pntrsumbnd  23507  nzss  30850
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