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Theorem biimpac 292
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 157 . 2 (𝜓 → (𝜑𝜒))
32imp 122 1 ((𝜓𝜑) → 𝜒)
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  2660  ordtri2or2exmidlem  4317  onsucelsucexmidlem  4320  ordsuc  4354  onsucuni2  4355  poltletr  4801  tz6.12-1  5296  nfunsn  5303  nnaordex  6240  th3qlem1  6348  ssfilem  6545  diffitest  6557  nqnq0pi  6944  distrlem1prl  7088  distrlem1pru  7089  eqle  7523  flodddiv4  10840
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