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 → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
Assertion	anabsi7	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabsi7.1	⊢ ( 𝜓 → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
2	1	anabsi6	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 )
3	2	ancoms	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )