Metamath Proof Explorer


Theorem relcmd

Description: The set of colimits of a diagram is a relation. (Contributed by Zhi Wang, 13-Nov-2025)

Ref Expression
Assertion relcmd Could not format assertion : No typesetting found for |- Rel ( ( C Colimit D ) ` F ) with typecode |-

Proof

Step Hyp Ref Expression
1 relup Could not format Rel ( ( C DiagFunc D ) ( C UP ( D FuncCat C ) ) F ) : No typesetting found for |- Rel ( ( C DiagFunc D ) ( C UP ( D FuncCat C ) ) F ) with typecode |-
2 cmdfval2 Could not format ( ( C Colimit D ) ` F ) = ( ( C DiagFunc D ) ( C UP ( D FuncCat C ) ) F ) : No typesetting found for |- ( ( C Colimit D ) ` F ) = ( ( C DiagFunc D ) ( C UP ( D FuncCat C ) ) F ) with typecode |-
3 2 releqi Could not format ( Rel ( ( C Colimit D ) ` F ) <-> Rel ( ( C DiagFunc D ) ( C UP ( D FuncCat C ) ) F ) ) : No typesetting found for |- ( Rel ( ( C Colimit D ) ` F ) <-> Rel ( ( C DiagFunc D ) ( C UP ( D FuncCat C ) ) F ) ) with typecode |-
4 1 3 mpbir Could not format Rel ( ( C Colimit D ) ` F ) : No typesetting found for |- Rel ( ( C Colimit D ) ` F ) with typecode |-