Theorem relopabv

Description: A class of ordered pairs is a relation. For a version without a disjoint variable condition, but using ax-11 and ax-12 , see relopab . (Contributed by SN, 8-Sep-2024)

	Ref	Expression
Assertion	relopabv	$$⊢\mathrm{Rel}\left\{⟨x,y⟩|\phi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\left\{⟨x,y⟩|\phi \right\}=\left\{⟨x,y⟩|\phi \right\}$$
2	1	relopabiv	$$⊢\mathrm{Rel}\left\{⟨x,y⟩|\phi \right\}$$