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Theorem anabsan 517
Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996.) (Revised by NM, 18-Nov-2013.)
Hypothesis
Ref Expression
anabsan.1 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
Assertion
Ref Expression
anabsan ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsan
StepHypRef Expression
1 pm4.24 381 . 2 (𝜑 ↔ (𝜑𝜑))
2 anabsan.1 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
31, 2sylanb 272 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  anabss1  518  anabss5  520  anandis  534  iddvds  10120  1dvds  10121
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