This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ Rel Ref$

Step	Hyp	Ref	Expression
1		df-ref	$⊢ Ref = \{⟨x, y⟩ \| (⋃ y = ⋃ x \land \forall z \in x \exists w \in y z \subseteq w)\}$
2	1	relopabiv	$⊢ Rel Ref$