Definition df-fdiv 45772

Description: Define the division of two functions into the complex numbers. (Contributed by AV, 15-May-2020.)

Assertion

Ref	Expression
df-fdiv	⊢ /f = (𝑓 ∈ V, 𝑔 ∈ V ↦ ((𝑓 ∘f / 𝑔) ↾ (𝑔 supp 0)))

Distinct variable group:   𝑓,𝑔

Detailed syntax breakdown of Definition df-fdiv

Step	Hyp	Ref	Expression
1		cfdiv 45771	. 2 class /f
2		vf	. . 3 setvar 𝑓
3		vg	. . 3 setvar 𝑔
4		cvv 3422	. . 3 class V
5	2	cv 1538	. . . . 5 class 𝑓
6	3	cv 1538	. . . . 5 class 𝑔
7		cdiv 11562	. . . . . 6 class /
8	7	cof 7509	. . . . 5 class ∘f /
9	5, 6, 8	co 7255	. . . 4 class (𝑓 ∘f / 𝑔)
10		cc0 10802	. . . . 5 class 0
11		csupp 7948	. . . . 5 class supp
12	6, 10, 11	co 7255	. . . 4 class (𝑔 supp 0)
13	9, 12	cres 5582	. . 3 class ((𝑓 ∘f / 𝑔) ↾ (𝑔 supp 0))
14	2, 3, 4, 4, 13	cmpo 7257	. 2 class (𝑓 ∈ V, 𝑔 ∈ V ↦ ((𝑓 ∘f / 𝑔) ↾ (𝑔 supp 0)))
15	1, 14	wceq 1539	1 wff /f = (𝑓 ∈ V, 𝑔 ∈ V ↦ ((𝑓 ∘f / 𝑔) ↾ (𝑔 supp 0)))

This definition is referenced by:  fdivval  45773