Definition df-sub 8245

Description: Define subtraction. Theorem subval 8264 shows its value (and describes how this definition works), Theorem subaddi 8359 relates it to addition, and Theorems subcli 8348 and resubcli 8335 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 8243	. 2 class -
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cc 7923	. . 3 class CC
5	3	cv 1372	. . . . . 6 class y
6		vz	. . . . . . 7 setvar z
7	6	cv 1372	. . . . . 6 class z
8		caddc 7928	. . . . . 6 class +
9	5, 7, 8	co 5944	. . . . 5 class ( y + z )
10	2	cv 1372	. . . . 5 class x
11	9, 10	wceq 1373	. . . 4 wff ( y + z ) = x
12	11, 6, 4	crio 5898	. . 3 class ( iota_ z e. CC ( y + z ) = x )
13	2, 3, 4, 4, 12	cmpo 5946	. 2 class ( x e. CC , y e. CC |-> ( iota_ z e. CC ( y + z ) = x ) )
14	1, 13	wceq 1373	1 wff - = ( x e. CC , y e. CC |-> ( iota_ z e. CC ( y + z ) = x ) )

This definition is referenced by:  subval  8264  subf  8274  cndsex  14315