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Theorem anabss1 518
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)
Hypothesis
Ref Expression
anabss1.1 (((𝜑𝜓) ∧ 𝜑) → 𝜒)
Assertion
Ref Expression
anabss1 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabss1
StepHypRef Expression
1 anabss1.1 . . 3 (((𝜑𝜓) ∧ 𝜑) → 𝜒)
21an32s 510 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
32anabsan 517 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:  anabss4  519
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