ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sylanr1 Structured version   GIF version

Theorem sylanr1 384
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr1.1 (φχ)
sylanr1.2 ((ψ (χ θ)) → τ)
Assertion
Ref Expression
sylanr1 ((ψ (φ θ)) → τ)

Proof of Theorem sylanr1
StepHypRef Expression
1 sylanr1.1 . . 3 (φχ)
21anim1i 323 . 2 ((φ θ) → (χ θ))
3 sylanr1.2 . 2 ((ψ (χ θ)) → τ)
42, 3sylan2 270 1 ((ψ (φ θ)) → τ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
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 is referenced by:  adantrll  453  adantrlr  454
  Copyright terms: Public domain W3C validator