Definition df-abs 10771

Description: Define the function for the absolute value (modulus) of a complex number. (Contributed by NM, 27-Jul-1999.)

Assertion

Ref	Expression
df-abs	|- abs = ( x e. CC |-> ( sqr ` ( x x. ( * ` x ) ) ) )

Detailed syntax breakdown of Definition df-abs

Step	Hyp	Ref	Expression
1		cabs 10769	. 2 class abs
2		vx	. . 3 setvar x
3		cc 7618	. . 3 class CC
4	2	cv 1330	. . . . 5 class x
5		ccj 10611	. . . . . 6 class *
6	4, 5	cfv 5123	. . . . 5 class ( * ` x )
7		cmul 7625	. . . . 5 class x.
8	4, 6, 7	co 5774	. . . 4 class ( x x. ( * ` x ) )
9		csqrt 10768	. . . 4 class sqr
10	8, 9	cfv 5123	. . 3 class ( sqr ` ( x x. ( * ` x ) ) )
11	2, 3, 10	cmpt 3989	. 2 class ( x e. CC |-> ( sqr ` ( x x. ( * ` x ) ) ) )
12	1, 11	wceq 1331	1 wff abs = ( x e. CC |-> ( sqr ` ( x x. ( * ` x ) ) ) )

This definition is referenced by:  absval  10773  absf  10882