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	|- ( R ErALTV A -> MembPart A )

Proof

Step	Hyp	Ref	Expression
1		mainer	|- ( R ErALTV A -> CoMembEr A )
2		mpet	|- ( MembPart A <-> CoMembEr A )
3	1 2	sylibr	|- ( R ErALTV A -> MembPart A )