Theorem cjmulrcli

Description: A complex number times its conjugate is real. (Contributed by NM, 11-May-1999)

	Ref	Expression
Hypothesis	recl.1	|- A e. CC
Assertion	cjmulrcli	|- ( A x. ( * ` A ) ) e. RR

Proof

Step	Hyp	Ref	Expression
1		recl.1	|- A e. CC
2		cjmulrcl	|- ( A e. CC -> ( A x. ( * ` A ) ) e. RR )
3	1 2	ax-mp	|- ( A x. ( * ` A ) ) e. RR