Definition df-homf 16331

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	|- Hom f = ( c e. _V |-> ( x e. ( Base ` c ) , y e. ( 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 16327	. 2 class Hom f
2		vc	. . 3 setvar c
3		cvv 3200	. . 3 class _V
4		vx	. . . 4 setvar x
5		vy	. . . 4 setvar y
6	2	cv 1482	. . . . 5 class c
7		cbs 15857	. . . . 5 class Base
8	6, 7	cfv 5888	. . . 4 class ( Base ` c )
9	4	cv 1482	. . . . 5 class x
10	5	cv 1482	. . . . 5 class y
11		chom 15952	. . . . . 6 class Hom
12	6, 11	cfv 5888	. . . . 5 class ( Hom ` c )
13	9, 10, 12	co 6650	. . . 4 class ( x ( Hom ` c ) y )
14	4, 5, 8, 8, 13	cmpt2 6652	. . 3 class ( x e. ( Base ` c ) , y e. ( Base ` c ) |-> ( x ( Hom ` c ) y ) )
15	2, 3, 14	cmpt 4729	. 2 class ( c e. _V |-> ( x e. ( Base ` c ) , y e. ( Base ` c ) |-> ( x ( Hom ` c ) y ) ) )
16	1, 15	wceq 1483	1 wff Hom f = ( c e. _V |-> ( x e. ( Base ` c ) , y e. ( Base ` c ) |-> ( x ( Hom ` c ) y ) ) )

This definition is referenced by:  homffval  16350