Definition df-sub 8462

Description: Define subtraction. Theorem subval 8481 shows its value (and describes how this definition works), Theorem subaddi 8576 relates it to addition, and Theorems subcli 8565 and resubcli 8552 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 8460	. 2 class -
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cc 8141	. . 3 class CC
5	3	cv 1397	. . . . . 6 class y
6		vz	. . . . . . 7 setvar z
7	6	cv 1397	. . . . . 6 class z
8		caddc 8146	. . . . . 6 class +
9	5, 7, 8	co 6058	. . . . 5 class ( y + z )
10	2	cv 1397	. . . . 5 class x
11	9, 10	wceq 1398	. . . 4 wff ( y + z ) = x
12	11, 6, 4	crio 6010	. . 3 class ( iota_ z e. CC ( y + z ) = x )
13	2, 3, 4, 4, 12	cmpo 6060	. 2 class ( x e. CC , y e. CC |-> ( iota_ z e. CC ( y + z ) = x ) )
14	1, 13	wceq 1398	1 wff - = ( x e. CC , y e. CC |-> ( iota_ z e. CC ( y + z ) = x ) )

This definition is referenced by:  subval  8481  subf  8491  cndsex  14827