Theorem dfdisjs4

Description: Alternate definition of the class of disjoints. (Contributed by Peter Mazsa, 5-Sep-2021)

	Ref	Expression
Assertion	dfdisjs4	$$⊢\mathrm{Disjs}=\left\{r\in \mathrm{Rels}|\forall x{\exists }^{*}uurx\right\}$$

Proof

Step	Hyp	Ref	Expression
1		dfdisjs2	$$⊢\mathrm{Disjs}=\left\{r\in \mathrm{Rels}|\wr r^{-1}\subseteq \mathrm{I}\right\}$$
2		cosscnvssid4	$$⊢\wr r^{-1}\subseteq \mathrm{I}\leftrightarrow \forall x{\exists }^{*}uurx$$
3	1 2	rabbieq	$$⊢\mathrm{Disjs}=\left\{r\in \mathrm{Rels}|\forall x{\exists }^{*}uurx\right\}$$