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Theorem anabsi7 555
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)
Hypothesis
Ref Expression
anabsi7.1 (𝜓 → ((𝜑𝜓) → 𝜒))
Assertion
Ref Expression
anabsi7 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsi7
StepHypRef Expression
1 anabsi7.1 . . 3 (𝜓 → ((𝜑𝜓) → 𝜒))
21anabsi6 554 . 2 ((𝜓𝜑) → 𝜒)
32ancoms 266 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:  syl2an23an  1262  nelrdva  2864  elunii  3711  ordelord  4273  onsucuni2  4449  funfveu  5402  fvelrn  5519  phplem3g  6718  prdisj  7268  gcdmultiplez  11621  dvdssq  11631
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