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Theorem exbiri 377
Description: Inference form of exbir 1395. (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 293 . 2 (((𝜑𝜓) ∧ 𝜃) → 𝜒)
32exp31 359 1 (𝜑 → (𝜓 → (𝜃𝜒)))
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  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  biimp3ar  1307  eqrdav  2114  tfrlem9  6182  sbthlem1  6811  lbreu  8660  uzsubsubfz  9767  elfzodifsumelfzo  9918  cncfmptid  12647  addccncf  12650  negcncf  12652
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