Definition df-fdiv 42332

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

Assertion

Ref	Expression
df-fdiv	|- /_f = ( f e. _V , g e. _V |-> ( ( f oF / g ) |` ( g supp 0 ) ) )

Distinct variable group:   f, g

Detailed syntax breakdown of Definition df-fdiv

Step	Hyp	Ref	Expression
1		cfdiv 42331	. 2 class /_f
2		vf	. . 3 setvar f
3		vg	. . 3 setvar g
4		cvv 3200	. . 3 class _V
5	2	cv 1482	. . . . 5 class f
6	3	cv 1482	. . . . 5 class g
7		cdiv 10684	. . . . . 6 class /
8	7	cof 6895	. . . . 5 class oF /
9	5, 6, 8	co 6650	. . . 4 class ( f oF / g )
10		cc0 9936	. . . . 5 class 0
11		csupp 7295	. . . . 5 class supp
12	6, 10, 11	co 6650	. . . 4 class ( g supp 0 )
13	9, 12	cres 5116	. . 3 class ( ( f oF / g ) |` ( g supp 0 ) )
14	2, 3, 4, 4, 13	cmpt2 6652	. 2 class ( f e. _V , g e. _V |-> ( ( f oF / g ) |` ( g supp 0 ) ) )
15	1, 14	wceq 1483	1 wff /_f = ( f e. _V , g e. _V |-> ( ( f oF / g ) |` ( g supp 0 ) ) )

This definition is referenced by:  fdivval  42333