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Theorem anabsan 549
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 pm4.24 392 . 2 (𝜑 ↔ (𝜑𝜑))
2 anabsan.1 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
31, 2sylanb 282 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anabss1  550  anabss5  552  anandis  566  iddvds  11433  1dvds  11434
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