ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl3anr3 Structured version   GIF version

Theorem syl3anr3 1188
Description: A syllogism inference. (Contributed by NM, 23-Aug-2007.)
Hypotheses
Ref Expression
syl3anr3.1 (φτ)
syl3anr3.2 ((χ (ψ θ τ)) → η)
Assertion
Ref Expression
syl3anr3 ((χ (ψ θ φ)) → η)

Proof of Theorem syl3anr3
StepHypRef Expression
1 syl3anr3.1 . . 3 (φτ)
213anim3i 1091 . 2 ((ψ θ φ) → (ψ θ τ))
3 syl3anr3.2 . 2 ((χ (ψ θ τ)) → η)
42, 3sylan2 270 1 ((χ (ψ θ φ)) → η)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 886
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator