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Metamath Proof Explorer

Theorem adantl

Description: Inference adding a conjunct to the left of an antecedent. (Contributed by NM, 30-Aug-1993) (Proof shortened by Wolf Lammen, 23-Nov-2012)

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

Proof

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