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Metamath Proof Explorer

Theorem relcoss

Description: Cosets by R is a relation. (Contributed by Peter Mazsa, 27-Dec-2018)

Ref Expression
Assertion relcoss Rel ≀ 𝑅

Proof

Step Hyp Ref Expression
1 df-coss ⊢ ≀ 𝑅 = { ⟨ 𝑥 , 𝑦 ⟩ ∣ ∃ 𝑢 ( 𝑢 𝑅 𝑥 ∧ 𝑢 𝑅 𝑦 ) }
2 1 relopabiv ⊢ Rel ≀ 𝑅