Definition df-homf 16943

Description: Define the functionalized Hom-set operator, which is exactly like Hom but is guaranteed to be a function on the base. (Contributed by Mario Carneiro, 4-Jan-2017.)

Assertion

Ref	Expression
df-homf	⊢ Homf = (𝑐 ∈ V ↦ (𝑥 ∈ (Base‘𝑐), 𝑦 ∈ (Base‘𝑐) ↦ (𝑥(Hom ‘𝑐)𝑦)))

Distinct variable group:   𝑥,𝑐,𝑦

Detailed syntax breakdown of Definition df-homf

Step	Hyp	Ref	Expression
1		chomf 16939	. 2 class Homf
2		vc	. . 3 setvar 𝑐
3		cvv 3496	. . 3 class V
4		vx	. . . 4 setvar 𝑥
5		vy	. . . 4 setvar 𝑦
6	2	cv 1536	. . . . 5 class 𝑐
7		cbs 16485	. . . . 5 class Base
8	6, 7	cfv 6357	. . . 4 class (Base‘𝑐)
9	4	cv 1536	. . . . 5 class 𝑥
10	5	cv 1536	. . . . 5 class 𝑦
11		chom 16578	. . . . . 6 class Hom
12	6, 11	cfv 6357	. . . . 5 class (Hom ‘𝑐)
13	9, 10, 12	co 7158	. . . 4 class (𝑥(Hom ‘𝑐)𝑦)
14	4, 5, 8, 8, 13	cmpo 7160	. . 3 class (𝑥 ∈ (Base‘𝑐), 𝑦 ∈ (Base‘𝑐) ↦ (𝑥(Hom ‘𝑐)𝑦))
15	2, 3, 14	cmpt 5148	. 2 class (𝑐 ∈ V ↦ (𝑥 ∈ (Base‘𝑐), 𝑦 ∈ (Base‘𝑐) ↦ (𝑥(Hom ‘𝑐)𝑦)))
16	1, 15	wceq 1537	1 wff Homf = (𝑐 ∈ V ↦ (𝑥 ∈ (Base‘𝑐), 𝑦 ∈ (Base‘𝑐) ↦ (𝑥(Hom ‘𝑐)𝑦)))

This definition is referenced by:  homffval  16962