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Theorem anabss1 890
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 881 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
32anabsan 889 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 197  df-an 385
This theorem is referenced by:  anabss4  891  ordtri3or  5916  onfununi  7608  omordi  7817  oeoelem  7849  hashssdif  13412  nzss  39036  stirlinglem5  40816
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