Theorem reloprab

Description: An operation class abstraction is a relation. (Contributed by NM, 16-Jun-2004)

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

Proof

Step	Hyp	Ref	Expression
1		dfoprab2	$$⊢\left\{⟨⟨x,y⟩,z⟩|\phi \right\}=\left\{⟨w,z⟩|\exists x\exists y\left(w=⟨x,y⟩\wedge \phi \right)\right\}$$
2	1	relopabiv	$$⊢\mathrm{Rel}\left\{⟨⟨x,y⟩,z⟩|\phi \right\}$$