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Theorem anabss5 789
Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss5.1 ((φ (φ ψ)) → χ)
Assertion
Ref Expression
anabss5 ((φ ψ) → χ)

Proof of Theorem anabss5
StepHypRef Expression
1 anabss5.1 . . 3 ((φ (φ ψ)) → χ)
21anassrs 629 . 2 (((φ φ) ψ) → χ)
32anabsan 786 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:  anabsi5  790
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