Theorem anabss7

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 19-Nov-2013)

	Ref	Expression
Hypothesis	anabss7.1	⊢ ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜒 )
Assertion	anabss7	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabss7.1	⊢ ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜒 )
2	1	anassrs	⊢ ( ( ( 𝜓 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 )
3	2	anabss4	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )