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Theorem biimpac 298
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 159 . 2 (𝜓 → (𝜑𝜒))
32imp 124 1 ((𝜓𝜑) → 𝜒)
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  2784  ordtri2or2exmidlem  4521  onsucelsucexmidlem  4524  ordsuc  4558  onsucuni2  4559  poltletr  5024  tz6.12-1  5537  nfunsn  5544  nnaordex  6522  th3qlem1  6630  ssfilem  6868  diffitest  6880  nqnq0pi  7415  distrlem1prl  7559  distrlem1pru  7560  eqle  8026  flodddiv4  11909  zabsle1  14033
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