Definition df-cj 6699

Description: Define the complex conjugate function. See cjcl 6714 for its closure and cjvalt 6710 for its value.

Assertion

Ref	Expression
df-cj	|- * = {<.x, y>. | (x e. CC /\ y = ((Re` x) - (i x. (Im` x))))}

Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-cj

Step	Hyp	Ref	Expression
1		ccj 6695	. 2 class *
2		vx	. . . . . 6 set x
3	2	cv 954	. . . . 5 class x
4		cc 5215	. . . . 5 class CC
5	3, 4	wcel 957	. . . 4 wff x e. CC
6		vy	. . . . . 6 set y
7	6	cv 954	. . . . 5 class y
8		cre 6693	. . . . . . 7 class Re
9	3, 8	cfv 3178	. . . . . 6 class (Re` x)
10		ci 5219	. . . . . . 7 class i
11		cim 6694	. . . . . . . 8 class Im
12	3, 11	cfv 3178	. . . . . . 7 class (Im` x)
13		cmul 5222	. . . . . . 7 class x.
14	10, 12, 13	co 3958	. . . . . 6 class (i x. (Im` x))
15		cmin 5275	. . . . . 6 class -
16	9, 14, 15	co 3958	. . . . 5 class ((Re` x) - (i x. (Im` x)))
17	7, 16	wceq 955	. . . 4 wff y = ((Re` x) - (i x. (Im` x)))
18	5, 17	wa 223	. . 3 wff (x e. CC /\ y = ((Re` x) - (i x. (Im` x))))
19	18, 2, 6	copab 2662	. 2 class {<.x, y>. | (x e. CC /\ y = ((Re` x) - (i x. (Im` x))))}
20	1, 19	wceq 955	1 wff * = {<.x, y>. | (x e. CC /\ y = ((Re` x) - (i x. (Im` x))))}

This definition is referenced by:  cjvalt 6710  cjcncf 7230

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