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Theorem biimpac 292
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 157 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
32imp 122 1  |-  ( ( ps  /\  ph )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  gencbvex2  2647  ordtri2or2exmidlem  4277  onsucelsucexmidlem  4280  ordsuc  4314  onsucuni2  4315  poltletr  4755  tz6.12-1  5232  nfunsn  5239  nnaordex  6166  th3qlem1  6274  ssfilem  6410  diffitest  6421  nqnq0pi  6690  distrlem1prl  6834  distrlem1pru  6835  eqle  7269  flodddiv4  10478
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