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Theorem biimpac 294
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 158 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
32imp 123 1  |-  ( ( ps  /\  ph )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  gencbvex2  2705  ordtri2or2exmidlem  4409  onsucelsucexmidlem  4412  ordsuc  4446  onsucuni2  4447  poltletr  4907  tz6.12-1  5414  nfunsn  5421  nnaordex  6389  th3qlem1  6497  ssfilem  6735  diffitest  6747  nqnq0pi  7210  distrlem1prl  7354  distrlem1pru  7355  eqle  7819  flodddiv4  11538
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