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Theorem anabsan 786
Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996.)
Hypothesis
Ref Expression
anabsan.1 (((φ φ) ψ) → χ)
Assertion
Ref Expression
anabsan ((φ ψ) → χ)

Proof of Theorem anabsan
StepHypRef Expression
1 pm4.24 624 . 2 (φ ↔ (φ φ))
2 anabsan.1 . 2 (((φ φ) ψ) → χ)
31, 2sylanb 458 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:  anabss1  787  anabss5  789  anandis  803
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