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Metamath Proof Explorer

Theorem anabsi5

Description: Absorption of antecedent into conjunction. (Contributed by NM, 11-Jun-1995) (Proof shortened by Wolf Lammen, 18-Nov-2013)

		Ref	Expression
	Hypothesis	anabsi5.1	$⊢ φ \to ((φ \land ψ) \to χ)$
	Assertion	anabsi5	$⊢ (φ \land ψ) \to χ$

Step	Hyp	Ref	Expression
1		anabsi5.1	$⊢ φ \to ((φ \land ψ) \to χ)$
2		simpl	$⊢ (φ \land ψ) \to φ$
3	2 1	mpcom	$⊢ (φ \land ψ) \to χ$