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	⊢ ( ( Rel 𝑅 ∧ 𝐴 𝑅 𝐵 ) → 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		brrelex12	⊢ ( ( Rel 𝑅 ∧ 𝐴 𝑅 𝐵 ) → ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) )
2	1	simpld	⊢ ( ( Rel 𝑅 ∧ 𝐴 𝑅 𝐵 ) → 𝐴 ∈ V )