Theorem brrelex2

Description: If two classes are related by a binary relation, then the second class is a set. (Contributed by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Assertion	brrelex2	$$⊢\left(\mathrm{Rel}R\wedge ARB\right)\to B\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		brrelex12	$$⊢\left(\mathrm{Rel}R\wedge ARB\right)\to \left(A\in \mathrm{V}\wedge B\in \mathrm{V}\right)$$
2	1	simprd	$$⊢\left(\mathrm{Rel}R\wedge ARB\right)\to B\in \mathrm{V}$$