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Theorem anabss5 647
 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 453 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
32anabsan 644 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 197  df-an 383 This theorem is referenced by:  anabsi5  648  syl2an2rOLD  665  mp3an2ani  1579  sq01  13193  faclbnd5  13289  hashssdif  13402  eqbrrdv2  34671  expgrowthi  39058  bccbc  39070  hoidmvlelem2  41327
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