Metamath Proof Explorer


Theorem det0

Description: The cosets by the null class are in equivalence relation if and only if the null class is disjoint (which it is, see disjALTV0 ). (Contributed by Peter Mazsa, 31-Dec-2021)

Ref Expression
Assertion det0
|- ( Disj (/) <-> EqvRel ,~ (/) )

Proof

Step Hyp Ref Expression
1 disjALTV0
 |-  Disj (/)
2 1 detlem
 |-  ( Disj (/) <-> EqvRel ,~ (/) )