ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl3an3br GIF version

Theorem syl3an3br 1211
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an3br.1 (𝜃𝜑)
syl3an3br.2 ((𝜓𝜒𝜃) → 𝜏)
Assertion
Ref Expression
syl3an3br ((𝜓𝜒𝜑) → 𝜏)

Proof of Theorem syl3an3br
StepHypRef Expression
1 syl3an3br.1 . . 3 (𝜃𝜑)
21biimpri 131 . 2 (𝜑𝜃)
3 syl3an3br.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an3 1205 1 ((𝜓𝜒𝜑) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  w3a 920
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  df-3an 922
This theorem is referenced by:  opelrng  4594
  Copyright terms: Public domain W3C validator