Metamath Proof Explorer

Theorem lmdrcl

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

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

Proof

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