Metamath Proof Explorer


Theorem termcthin

Description: A terminal category is a thin category. (Contributed by Zhi Wang, 16-Oct-2025)

Ref Expression
Assertion termcthin Could not format assertion : No typesetting found for |- ( C e. TermCat -> C e. ThinCat ) with typecode |-

Proof

Step Hyp Ref Expression
1 eqid Base C = Base C
2 1 istermc Could not format ( C e. TermCat <-> ( C e. ThinCat /\ E. x ( Base ` C ) = { x } ) ) : No typesetting found for |- ( C e. TermCat <-> ( C e. ThinCat /\ E. x ( Base ` C ) = { x } ) ) with typecode |-
3 2 simplbi Could not format ( C e. TermCat -> C e. ThinCat ) : No typesetting found for |- ( C e. TermCat -> C e. ThinCat ) with typecode |-