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Theorem anabss7 572
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 19-Nov-2013.)
Hypothesis
Ref Expression
anabss7.1 ((𝜓 ∧ (𝜑𝜓)) → 𝜒)
Assertion
Ref Expression
anabss7 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabss7
StepHypRef Expression
1 anabss7.1 . . 3 ((𝜓 ∧ (𝜑𝜓)) → 𝜒)
21anassrs 397 . 2 (((𝜓𝜑) ∧ 𝜓) → 𝜒)
32anabss4 566 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anabsan2  573  syl2an2  583  funbrfv  5460  lcmcllem  11755
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