Theorem lmdrcl

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

	Ref	Expression
Assertion	lmdrcl	⊢ ( 𝑋 ∈ ( ( 𝐶 Limit 𝐷 ) ‘ 𝐹 ) → 𝐹 ∈ ( 𝐷 Func 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		lmdfval	⊢ ( 𝐶 Limit 𝐷 ) = ( 𝑓 ∈ ( 𝐷 Func 𝐶 ) ↦ ( ( oppFunc ‘ ( 𝐶 Δfunc 𝐷 ) ) ( ( oppCat ‘ 𝐶 ) UP ( oppCat ‘ ( 𝐷 FuncCat 𝐶 ) ) ) 𝑓 ) )
2	1	mptrcl	⊢ ( 𝑋 ∈ ( ( 𝐶 Limit 𝐷 ) ‘ 𝐹 ) → 𝐹 ∈ ( 𝐷 Func 𝐶 ) )