Theorem reldmran

Description: The domain of Ran is a relation. (Contributed by Zhi Wang, 4-Nov-2025)

	Ref	Expression
Assertion	reldmran	⊢ Rel dom Ran

Proof

Step	Hyp	Ref	Expression
1		df-ran	⊢ Ran = ( 𝑝 ∈ ( V × V ) , 𝑒 ∈ V ↦ ⦋ ( 1st ‘ 𝑝 ) / 𝑐 ⦌ ⦋ ( 2nd ‘ 𝑝 ) / 𝑑 ⦌ ( 𝑓 ∈ ( 𝑐 Func 𝑑 ) , 𝑥 ∈ ( 𝑐 Func 𝑒 ) ↦ ( ( oppFunc ‘ ( ⟨ 𝑑 , 𝑒 ⟩ −∘F 𝑓 ) ) ( ( oppCat ‘ ( 𝑑 FuncCat 𝑒 ) ) UP ( oppCat ‘ ( 𝑐 FuncCat 𝑒 ) ) ) 𝑥 ) ) )
2	1	reldmmpo	⊢ Rel dom Ran