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Theorem anabss3 673
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss3.1 (((𝜑𝜓) ∧ 𝜓) → 𝜒)
Assertion
Ref Expression
anabss3 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabss3
StepHypRef Expression
1 anabss3.1 . . 3 (((𝜑𝜓) ∧ 𝜓) → 𝜒)
21anasss 469 . 2 ((𝜑 ∧ (𝜓𝜓)) → 𝜒)
32anabsan2 672 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398
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 209  df-an 399
This theorem is referenced by:  3anidm23  1417  expclzlem  13434  plyrem  24876  loop1cycl  32388  anabss7p1  41272
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