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Theorem exbiri 368
Description: Inference form of exbir 1341. (Contributed by Alan Sare, 31-Dec-2011.) (Proof shortened by Wolf Lammen, 27-Jan-2013.)
Hypothesis
Ref Expression
exbiri.1 ((𝜑𝜓) → (𝜒𝜃))
Assertion
Ref Expression
exbiri (𝜑 → (𝜓 → (𝜃𝜒)))

Proof of Theorem exbiri
StepHypRef Expression
1 exbiri.1 . . 3 ((𝜑𝜓) → (𝜒𝜃))
21biimpar 285 . 2 (((𝜑𝜓) ∧ 𝜃) → 𝜒)
32exp31 350 1 (𝜑 → (𝜓 → (𝜃𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  biimp3ar  1252  eqrdav  2055  tfrlem9  5966  uzsubsubfz  9013  elfzodifsumelfzo  9159
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