Theorem anabss1

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 31-Dec-2012)

	Ref	Expression
Hypothesis	anabss1.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜑 ) → 𝜒 )
Assertion	anabss1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabss1.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜑 ) → 𝜒 )
2	1	an32s	⊢ ( ( ( 𝜑 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 )
3	2	anabsan	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )