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Metamath Proof Explorer

Theorem adantr

Description: Inference adding a conjunct to the right of an antecedent. (Contributed by NM, 30-Aug-1993)

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

Step	Hyp	Ref	Expression
1		adantr.1	$⊢ φ \to ψ$
2	1	a1d	$⊢ φ \to (χ \to ψ)$
3	2	imp	$⊢ (φ \land χ) \to ψ$