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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  2736  ordtri2or2exmidlem  4448  onsucelsucexmidlem  4451  ordsuc  4485  onsucuni2  4486  poltletr  4946  tz6.12-1  5455  nfunsn  5462  nnaordex  6430  th3qlem1  6538  ssfilem  6776  diffitest  6788  nqnq0pi  7269  distrlem1prl  7413  distrlem1pru  7414  eqle  7878  flodddiv4  11665
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