Definition df-sub 8126

Description: Define subtraction. Theorem subval 8145 shows its value (and describes how this definition works), Theorem subaddi 8240 relates it to addition, and Theorems subcli 8229 and resubcli 8216 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 8124	. 2 class -
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cc 7806	. . 3 class CC
5	3	cv 1352	. . . . . 6 class y
6		vz	. . . . . . 7 setvar z
7	6	cv 1352	. . . . . 6 class z
8		caddc 7811	. . . . . 6 class +
9	5, 7, 8	co 5872	. . . . 5 class ( y + z )
10	2	cv 1352	. . . . 5 class x
11	9, 10	wceq 1353	. . . 4 wff ( y + z ) = x
12	11, 6, 4	crio 5827	. . 3 class ( iota_ z e. CC ( y + z ) = x )
13	2, 3, 4, 4, 12	cmpo 5874	. 2 class ( x e. CC , y e. CC |-> ( iota_ z e. CC ( y + z ) = x ) )
14	1, 13	wceq 1353	1 wff - = ( x e. CC , y e. CC |-> ( iota_ z e. CC ( y + z ) = x ) )

This definition is referenced by:  subval  8145  subf  8155