Metamath Proof Explorer


Theorem reldmlmd2

Description: The domain of ( C Limit D ) is a relation. (Contributed by Zhi Wang, 14-Nov-2025)

Ref Expression
Assertion reldmlmd2 Could not format assertion : No typesetting found for |- Rel dom ( C Limit D ) with typecode |-

Proof

Step Hyp Ref Expression
1 relfunc Rel D Func C
2 ovex Could not format ( ( oppFunc ` ( C DiagFunc D ) ) ( ( oppCat ` C ) UP ( oppCat ` ( D FuncCat C ) ) ) f ) e. _V : No typesetting found for |- ( ( oppFunc ` ( C DiagFunc D ) ) ( ( oppCat ` C ) UP ( oppCat ` ( D FuncCat C ) ) ) f ) e. _V with typecode |-
3 lmdfval Could not format ( C Limit D ) = ( f e. ( D Func C ) |-> ( ( oppFunc ` ( C DiagFunc D ) ) ( ( oppCat ` C ) UP ( oppCat ` ( D FuncCat C ) ) ) f ) ) : No typesetting found for |- ( C Limit D ) = ( f e. ( D Func C ) |-> ( ( oppFunc ` ( C DiagFunc D ) ) ( ( oppCat ` C ) UP ( oppCat ` ( D FuncCat C ) ) ) f ) ) with typecode |-
4 2 3 dmmpti Could not format dom ( C Limit D ) = ( D Func C ) : No typesetting found for |- dom ( C Limit D ) = ( D Func C ) with typecode |-
5 4 releqi Could not format ( Rel dom ( C Limit D ) <-> Rel ( D Func C ) ) : No typesetting found for |- ( Rel dom ( C Limit D ) <-> Rel ( D Func C ) ) with typecode |-
6 1 5 mpbir Could not format Rel dom ( C Limit D ) : No typesetting found for |- Rel dom ( C Limit D ) with typecode |-