Metamath Proof Explorer


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 Could not format assertion : No typesetting found for |- ( R ErALTV A -> MembPart A ) with typecode |-

Proof

Step Hyp Ref Expression
1 mainer Could not format ( R ErALTV A -> CoMembEr A ) : No typesetting found for |- ( R ErALTV A -> CoMembEr A ) with typecode |-
2 mpet Could not format ( MembPart A <-> CoMembEr A ) : No typesetting found for |- ( MembPart A <-> CoMembEr A ) with typecode |-
3 1 2 sylibr Could not format ( R ErALTV A -> MembPart A ) : No typesetting found for |- ( R ErALTV A -> MembPart A ) with typecode |-