Theorem refrel

Description: Refinement is a relation. (Contributed by Jeff Hankins, 18-Jan-2010) (Revised by Thierry Arnoux, 3-Feb-2020)

	Ref	Expression
Assertion	refrel	$$⊢\mathrm{Rel}\mathrm{Ref}$$

Proof

Step	Hyp	Ref	Expression
1		df-ref	$$⊢\mathrm{Ref}=\left\{⟨x,y⟩|\left(\bigcup y=\bigcup x\wedge \forall z\in x\exists w\in yz\subseteq w\right)\right\}$$
2	1	relopabi	$$⊢\mathrm{Rel}\mathrm{Ref}$$