Theorem fences

Description: The Theorem of Fences by Equivalences: all conceivable equivalence relations (besides the comember equivalence relation cf. mpet ) generate a partition of the members. (Contributed by Peter Mazsa, 26-Sep-2021)

	Ref	Expression
Assertion	fences	$$⊢RErALTVA\to MembPartA$$

Proof

Step	Hyp	Ref	Expression
1		mainer	$$⊢RErALTVA\to CoMembErA$$
2		mpet	$$⊢MembPartA\leftrightarrow CoMembErA$$
3	1 2	sylibr	$$⊢RErALTVA\to MembPartA$$