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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 -1 = I
2 1 eqimssi ⊢ ≀ I -1 ⊆ I
3 reli ⊢ Rel ⁡ I
4 dfdisjALTV2 ⊢ Disj I ↔ ≀ I -1 ⊆ I ∧ Rel ⁡ I
5 2 3 4 mpbir2an ⊢ Disj I