Metamath Proof Explorer


Theorem anabsi7

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 18-Nov-2013)

Ref Expression
Hypothesis anabsi7.1 ( 𝜓 → ( ( 𝜑𝜓 ) → 𝜒 ) )
Assertion anabsi7 ( ( 𝜑𝜓 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 anabsi7.1 ( 𝜓 → ( ( 𝜑𝜓 ) → 𝜒 ) )
2 1 anabsi6 ( ( 𝜓𝜑 ) → 𝜒 )
3 2 ancoms ( ( 𝜑𝜓 ) → 𝜒 )