Metamath Proof Explorer


Theorem efmndbas0

Description: The base set of the monoid of endofunctions on the empty set is the singleton containing the empty set. (Contributed by AV, 27-Jan-2024) (Proof shortened by AV, 31-Mar-2024)

Ref Expression
Assertion efmndbas0 Could not format assertion : No typesetting found for |- ( Base ` ( EndoFMnd ` (/) ) ) = { (/) } with typecode |-

Proof

Step Hyp Ref Expression
1 eqid Could not format ( EndoFMnd ` (/) ) = ( EndoFMnd ` (/) ) : No typesetting found for |- ( EndoFMnd ` (/) ) = ( EndoFMnd ` (/) ) with typecode |-
2 eqid Could not format ( Base ` ( EndoFMnd ` (/) ) ) = ( Base ` ( EndoFMnd ` (/) ) ) : No typesetting found for |- ( Base ` ( EndoFMnd ` (/) ) ) = ( Base ` ( EndoFMnd ` (/) ) ) with typecode |-
3 1 2 efmndbas Could not format ( Base ` ( EndoFMnd ` (/) ) ) = ( (/) ^m (/) ) : No typesetting found for |- ( Base ` ( EndoFMnd ` (/) ) ) = ( (/) ^m (/) ) with typecode |-
4 0map0sn0 =
5 3 4 eqtri Could not format ( Base ` ( EndoFMnd ` (/) ) ) = { (/) } : No typesetting found for |- ( Base ` ( EndoFMnd ` (/) ) ) = { (/) } with typecode |-