Theorem brrelex1i

Description: The first argument of a binary relation exists. (An artifact of our ordered pair definition.) (Contributed by NM, 4-Jun-1998)

	Ref	Expression
Hypothesis	brrelexi.1	⊢ Rel 𝑅
Assertion	brrelex1i	⊢ ( 𝐴 𝑅 𝐵 → 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		brrelexi.1	⊢ Rel 𝑅
2		brrelex1	⊢ ( ( Rel 𝑅 ∧ 𝐴 𝑅 𝐵 ) → 𝐴 ∈ V )
3	1 2	mpan	⊢ ( 𝐴 𝑅 𝐵 → 𝐴 ∈ V )