Theorem anabsi6

Description: Absorption of antecedent into conjunction. (Contributed by NM, 14-Aug-2000)

	Ref	Expression
Hypothesis	anabsi6.1	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜑 ) → 𝜒 ) )
Assertion	anabsi6	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabsi6.1	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜑 ) → 𝜒 ) )
2	1	ancomsd	⊢ ( 𝜑 → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
3	2	anabsi5	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )