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Theorem anabsan2 526
Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.) (Revised by NM, 1-Jan-2013.)
Hypothesis
Ref Expression
anabsan2.1 ((𝜑 ∧ (𝜓𝜓)) → 𝜒)
Assertion
Ref Expression
anabsan2 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsan2
StepHypRef Expression
1 anabsan2.1 . . 3 ((𝜑 ∧ (𝜓𝜓)) → 𝜒)
21an12s 507 . 2 ((𝜓 ∧ (𝜑𝜓)) → 𝜒)
32anabss7 525 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:  anabss3  527  anandirs  535
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