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Theorem exbiri 374
Description: Inference form of exbir 1370. (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 291 . 2 (((𝜑𝜓) ∧ 𝜃) → 𝜒)
32exp31 356 1 (𝜑 → (𝜓 → (𝜃𝜒)))
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  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  biimp3ar  1282  eqrdav  2087  tfrlem9  6084  sbthlem1  6666  lbreu  8406  uzsubsubfz  9461  elfzodifsumelfzo  9612
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