Theorem brrelex2i

Description: The second argument of a binary relation exists. (An artifact of our ordered pair definition.) (Contributed by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Hypothesis	brrelexi.1	⊢ Rel 𝑅
Assertion	brrelex2i	⊢ ( 𝐴 𝑅 𝐵 → 𝐵 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		brrelexi.1	⊢ Rel 𝑅
2		brrelex2	⊢ ( ( Rel 𝑅 ∧ 𝐴 𝑅 𝐵 ) → 𝐵 ∈ V )
3	1 2	mpan	⊢ ( 𝐴 𝑅 𝐵 → 𝐵 ∈ V )