Theorem dfcomember2

Description: Alternate definition of the comember equivalence relation. (Contributed by Peter Mazsa, 25-Sep-2021)

	Ref	Expression
Assertion	dfcomember2	$$⊢CoMembErA\leftrightarrow \left(EqvRel\sim A\wedge \mathrm{dom}\sim A/\sim A=A\right)$$

Proof

Step	Hyp	Ref	Expression
1		dfcomember	$$⊢CoMembErA\leftrightarrow \sim AErALTVA$$
2		dferALTV2	$$⊢\sim AErALTVA\leftrightarrow \left(EqvRel\sim A\wedge \mathrm{dom}\sim A/\sim A=A\right)$$
3	1 2	bitri	$$⊢CoMembErA\leftrightarrow \left(EqvRel\sim A\wedge \mathrm{dom}\sim A/\sim A=A\right)$$