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	⊢ Rel 𝑅
Assertion	brrelex12i	⊢ ( 𝐴 𝑅 𝐵 → ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) )

Proof

Step	Hyp	Ref	Expression
1		brrelexi.1	⊢ Rel 𝑅
2		brrelex12	⊢ ( ( Rel 𝑅 ∧ 𝐴 𝑅 𝐵 ) → ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) )
3	1 2	mpan	⊢ ( 𝐴 𝑅 𝐵 → ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) )