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Theorem anabss5 852
Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss5.1 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
Assertion
Ref Expression
anabss5 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabss5
StepHypRef Expression
1 anabss5.1 . . 3 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
21anassrs 677 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
32anabsan 849 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  anabsi5  853  syl2an2r  871  mp3an2ani  1422  sq01  12805  faclbnd5  12904  hashssdif  13015  eqbrrdv2  32949  expgrowthi  37337  bccbc  37349  hoidmvlelem2  39269
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