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Theorem anabsan 849
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 pm4.24 672 . 2 (𝜑 ↔ (𝜑𝜑))
2 anabsan.1 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
31, 2sylanb 487 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  anabss1  850  anabss5  852  anandis  868  iddvds  14781  1dvds  14782
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