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

Proof

Step Hyp Ref Expression
1 df-ref Ref = { ⟨ 𝑥 , 𝑦 ⟩ ∣ ( 𝑦 = 𝑥 ∧ ∀ 𝑧𝑥𝑤𝑦 𝑧𝑤 ) }
2 1 relopabiv Rel Ref