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Theorem biimpac 298
Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.)
Hypothesis
Ref Expression
biimpa.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
biimpac  |-  ( ( ps  /\  ph )  ->  ch )

Proof of Theorem biimpac
StepHypRef Expression
1 biimpa.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21biimpcd 159 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
32imp 124 1  |-  ( ( ps  /\  ph )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  gencbvex2  2799  ordtri2or2exmidlem  4543  onsucelsucexmidlem  4546  ordsuc  4580  onsucuni2  4581  poltletr  5047  tz6.12-1  5561  nfunsn  5569  nnaordex  6553  th3qlem1  6663  ssfilem  6903  diffitest  6915  nqnq0pi  7467  distrlem1prl  7611  distrlem1pru  7612  eqle  8079  flodddiv4  11971  zabsle1  14858
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