Metamath Proof Explorer


Theorem relcoels

Description: Coelements on A is a relation. (Contributed by Peter Mazsa, 5-Oct-2021)

Ref Expression
Assertion relcoels Rel ∼ 𝐴

Proof

Step Hyp Ref Expression
1 relcoss Rel ≀ ( E ↾ 𝐴 )
2 df-coels 𝐴 = ≀ ( E ↾ 𝐴 )
3 2 releqi ( Rel ∼ 𝐴 ↔ Rel ≀ ( E ↾ 𝐴 ) )
4 1 3 mpbir Rel ∼ 𝐴