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Metamath Proof Explorer

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	$⊢ ((φ \land ψ) \land φ) \to χ$
	Assertion	anabss1	$⊢ (φ \land ψ) \to χ$

Step	Hyp	Ref	Expression
1		anabss1.1	$⊢ ((φ \land ψ) \land φ) \to χ$
2	1	an32s	$⊢ ((φ \land φ) \land ψ) \to χ$
3	2	anabsan	$⊢ (φ \land ψ) \to χ$