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	$$⊢\mathrm{Rel}R$$
Assertion	relelrni	$$⊢ARB\to B\in \mathrm{ran}R$$

Proof

Step	Hyp	Ref	Expression
1		releldm.1	$$⊢\mathrm{Rel}R$$
2		relelrn	$$⊢\left(\mathrm{Rel}R\wedge ARB\right)\to B\in \mathrm{ran}R$$
3	1 2	mpan	$$⊢ARB\to B\in \mathrm{ran}R$$