Theorem brrelex12i

Description: Two classes that are related by a binary relation are sets. Inference form. (Contributed by BJ, 3-Oct-2022)

	Ref	Expression
Hypothesis	brrelexi.1	$$⊢\mathrm{Rel}R$$
Assertion	brrelex12i	$$⊢ARB\to \left(A\in \mathrm{V}\wedge B\in \mathrm{V}\right)$$

Proof

Step	Hyp	Ref	Expression
1		brrelexi.1	$$⊢\mathrm{Rel}R$$
2		brrelex12	$$⊢\left(\mathrm{Rel}R\wedge ARB\right)\to \left(A\in \mathrm{V}\wedge B\in \mathrm{V}\right)$$
3	1 2	mpan	$$⊢ARB\to \left(A\in \mathrm{V}\wedge B\in \mathrm{V}\right)$$