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Theorem anabsi7 546
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 545 . 2 ((𝜓𝜑) → 𝜒)
32ancoms 264 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  syl2an23an  1231  nelrdva  2806  elunii  3626  ordelord  4164  onsucuni2  4335  funfveu  5239  fvelrn  5350  phplem3g  6412  prdisj  6779  gcdmultiplez  10600  dvdssq  10610
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