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Theorem anabsi6 545
Description: Absorption of antecedent into conjunction. (Contributed by NM, 14-Aug-2000.)
Hypothesis
Ref Expression
anabsi6.1 (𝜑 → ((𝜓𝜑) → 𝜒))
Assertion
Ref Expression
anabsi6 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsi6
StepHypRef Expression
1 anabsi6.1 . . 3 (𝜑 → ((𝜓𝜑) → 𝜒))
21ancomsd 265 . 2 (𝜑 → ((𝜑𝜓) → 𝜒))
32anabsi5 544 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:  anabsi7  546
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