Theorem anabsan2

Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004)

	Ref	Expression
Hypothesis	anabsan2.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜓 ) ) → 𝜒 )
Assertion	anabsan2	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabsan2.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜓 ) ) → 𝜒 )
2	1	an12s	⊢ ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜒 )
3	2	anabss7	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )