Definition df-sub 6981

Description: Define subtraction. Theorem subval 7000 shows its value (and describes how this definition works), theorem subaddi 7094 relates it to addition, and theorems subcli 7083 and resubcli 7070 prove its closure laws. (Contributed by NM, 26-Nov-1994.)

Assertion

Ref	Expression
df-sub	|- - = (x e. CC , y e. CC |-> ( iota_z e. CC (y + z) = x))

Distinct variable group:   x,y,z

Detailed syntax breakdown of Definition df-sub

Step	Hyp	Ref	Expression
1		cmin 6979	. 2 class -
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cc 6709	. . 3 class CC
5	3	cv 1241	. . . . . 6 class y
6		vz	. . . . . . 7 setvar z
7	6	cv 1241	. . . . . 6 class z
8		caddc 6714	. . . . . 6 class +
9	5, 7, 8	co 5455	. . . . 5 class (y + z)
10	2	cv 1241	. . . . 5 class x
11	9, 10	wceq 1242	. . . 4 wff (y + z) = x
12	11, 6, 4	crio 5410	. . 3 class ( iota_z e. CC (y + z) = x)
13	2, 3, 4, 4, 12	cmpt2 5457	. 2 class (x e. CC , y e. CC |-> ( iota_z e. CC (y + z) = x))
14	1, 13	wceq 1242	1 wff - = (x e. CC , y e. CC |-> ( iota_z e. CC (y + z) = x))

This definition is referenced by:  subval  7000  subf  7010