Metamath Proof Explorer

Theorem cmdrcl

Description: Reverse closure for a colimit of a diagram. (Contributed by Zhi Wang, 20-Nov-2025)

Ref Expression
Assertion cmdrcl 
|- ( X e. ( ( C Colimit D ) ` F ) -> F e. ( D Func C ) )

Proof

Step Hyp Ref Expression
1 cmdfval 
 |-  ( C Colimit D ) = ( f e. ( D Func C ) |-> ( ( C DiagFunc D ) ( C UP ( D FuncCat C ) ) f ) )
2 1 mptrcl 
 |-  ( X e. ( ( C Colimit D ) ` F ) -> F e. ( D Func C ) )