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Theorem biimpac 296
Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.)
Hypothesis
Ref Expression
biimpa.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
biimpac ((𝜓𝜑) → 𝜒)

Proof of Theorem biimpac
StepHypRef Expression
1 biimpa.1 . . 3 (𝜑 → (𝜓𝜒))
21biimpcd 158 . 2 (𝜓 → (𝜑𝜒))
32imp 123 1 ((𝜓𝜑) → 𝜒)
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  2777  ordtri2or2exmidlem  4510  onsucelsucexmidlem  4513  ordsuc  4547  onsucuni2  4548  poltletr  5011  tz6.12-1  5523  nfunsn  5530  nnaordex  6507  th3qlem1  6615  ssfilem  6853  diffitest  6865  nqnq0pi  7400  distrlem1prl  7544  distrlem1pru  7545  eqle  8011  flodddiv4  11893  zabsle1  13694
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