Theorem anabsi8

Description: Absorption of antecedent into conjunction. (Contributed by NM, 26-Sep-1999)

	Ref	Expression
Hypothesis	anabsi8.1	⊢ ( 𝜓 → ( ( 𝜓 ∧ 𝜑 ) → 𝜒 ) )
Assertion	anabsi8	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabsi8.1	⊢ ( 𝜓 → ( ( 𝜓 ∧ 𝜑 ) → 𝜒 ) )
2	1	anabsi5	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 )
3	2	ancoms	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )