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Metamath Proof Explorer

Theorem relelrni

Description: The second argument of a binary relation belongs to its range. (Contributed by NM, 28-Apr-2015)

		Ref	Expression
	Hypothesis	releldm.1	$⊢ Rel R$
	Assertion	relelrni	$⊢ A R B \to B \in ran R$

Step	Hyp	Ref	Expression
1		releldm.1	$⊢ Rel R$
2		relelrn	$⊢ (Rel R \land A R B) \to B \in ran R$
3	1 2	mpan	$⊢ A R B \to B \in ran R$