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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 ≀ ∅