NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  syl3anr2 GIF version

Theorem syl3anr2 1235
Description: A syllogism inference. (Contributed by NM, 1-Aug-2007.)
Hypotheses
Ref Expression
syl3anr2.1 (φθ)
syl3anr2.2 ((χ (ψ θ τ)) → η)
Assertion
Ref Expression
syl3anr2 ((χ (ψ φ τ)) → η)

Proof of Theorem syl3anr2
StepHypRef Expression
1 syl3anr2.1 . . 3 (φθ)
2 syl3anr2.2 . . . 4 ((χ (ψ θ τ)) → η)
32ancoms 439 . . 3 (((ψ θ τ) χ) → η)
41, 3syl3anl2 1231 . 2 (((ψ φ τ) χ) → η)
54ancoms 439 1 ((χ (ψ φ τ)) → η)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator