Theorem cjmulrcli

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

	Ref	Expression
Hypothesis	recl.1	$$⊢A\in ℂ$$
Assertion	cjmulrcli	$$⊢A\bar{A}\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		recl.1	$$⊢A\in ℂ$$
2		cjmulrcl	$$⊢A\in ℂ\to A\bar{A}\in ℝ$$
3	1 2	ax-mp	$$⊢A\bar{A}\in ℝ$$