Theorem brrelex1

Description: If two classes are related by a binary relation, then the first class is a set. (Contributed by NM, 18-May-2004) (Revised by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Assertion	brrelex1	$$⊢\left(\mathrm{Rel}R\wedge ARB\right)\to A\in \mathrm{V}$$

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	simpld	$$⊢\left(\mathrm{Rel}R\wedge ARB\right)\to A\in \mathrm{V}$$