Metamath Proof Explorer


Theorem disjALTVid

Description: The class of identity relations is disjoint. (Contributed by Peter Mazsa, 20-Jun-2021)

Ref Expression
Assertion disjALTVid Disj I

Proof

Step Hyp Ref Expression
1 cosscnvid I = I
2 1 eqimssi I ⊆ I
3 reli Rel I
4 dfdisjALTV2 ( Disj I ↔ ( ≀ I ⊆ I ∧ Rel I ) )
5 2 3 4 mpbir2an Disj I