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Theorem anabsan 662
Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996.)
Hypothesis
Ref Expression
anabsan.1 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
Assertion
Ref Expression
anabsan ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsan
StepHypRef Expression
1 pm4.24 564 . 2 (𝜑 ↔ (𝜑𝜑))
2 anabsan.1 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
31, 2sylanb 581 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 206  df-an 397
This theorem is referenced by:  anabss1  663  anabss5  665  anandis  675  iddvds  15979  1dvds  15980
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