Metamath Proof Explorer


Theorem detidres

Description: The cosets by the restricted identity relation are in equivalence relation if and only if the restricted identity relation is disjoint. (Contributed by Peter Mazsa, 31-Dec-2021)

Ref Expression
Assertion detidres ( Disj ( I ↾ 𝐴 ) ↔ EqvRel ≀ ( I ↾ 𝐴 ) )

Proof

Step Hyp Ref Expression
1 disjALTVidres Disj ( I ↾ 𝐴 )
2 1 detlem ( Disj ( I ↾ 𝐴 ) ↔ EqvRel ≀ ( I ↾ 𝐴 ) )