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Metamath Proof Explorer

Theorem anabsi7

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 18-Nov-2013)

		Ref	Expression
	Hypothesis	anabsi7.1	$⊢ ψ \to ((φ \land ψ) \to χ)$
	Assertion	anabsi7	$⊢ (φ \land ψ) \to χ$

Step	Hyp	Ref	Expression
1		anabsi7.1	$⊢ ψ \to ((φ \land ψ) \to χ)$
2	1	anabsi6	$⊢ (ψ \land φ) \to χ$
3	2	ancoms	$⊢ (φ \land ψ) \to χ$