Definition df-sub 8244

Description: Define subtraction. Theorem subval 8263 shows its value (and describes how this definition works), Theorem subaddi 8358 relates it to addition, and Theorems subcli 8347 and resubcli 8334 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 8242	. 2 class -
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cc 7922	. . 3 class CC
5	3	cv 1371	. . . . . 6 class y
6		vz	. . . . . . 7 setvar z
7	6	cv 1371	. . . . . 6 class z
8		caddc 7927	. . . . . 6 class +
9	5, 7, 8	co 5943	. . . . 5 class ( y + z )
10	2	cv 1371	. . . . 5 class x
11	9, 10	wceq 1372	. . . 4 wff ( y + z ) = x
12	11, 6, 4	crio 5897	. . 3 class ( iota_ z e. CC ( y + z ) = x )
13	2, 3, 4, 4, 12	cmpo 5945	. 2 class ( x e. CC , y e. CC |-> ( iota_ z e. CC ( y + z ) = x ) )
14	1, 13	wceq 1372	1 wff - = ( x e. CC , y e. CC |-> ( iota_ z e. CC ( y + z ) = x ) )

This definition is referenced by:  subval  8263  subf  8273  cndsex  14286