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Metamath Proof Explorer

Theorem anabss3

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 1-Jan-2013)

		Ref	Expression
	Hypothesis	anabss3.1	$⊢ ((φ \land ψ) \land ψ) \to χ$
	Assertion	anabss3	$⊢ (φ \land ψ) \to χ$

Step	Hyp	Ref	Expression
1		anabss3.1	$⊢ ((φ \land ψ) \land ψ) \to χ$
2	1	anasss	$⊢ (φ \land (ψ \land ψ)) \to χ$
3	2	anabsan2	$⊢ (φ \land ψ) \to χ$