NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  anabss3 GIF version

Theorem anabss3 796
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss3.1 (((φ ψ) ψ) → χ)
Assertion
Ref Expression
anabss3 ((φ ψ) → χ)

Proof of Theorem anabss3
StepHypRef Expression
1 anabss3.1 . . 3 (((φ ψ) ψ) → χ)
21anasss 628 . 2 ((φ (ψ ψ)) → χ)
32anabsan2 795 1 ((φ ψ) → χ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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
This theorem is referenced by:  3anidm23  1241
  Copyright terms: Public domain W3C validator