Theorem cjmulge0d

Description: A complex number times its conjugate is nonnegative. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	recld.1	$$⊢\phi \to A\in ℂ$$
Assertion	cjmulge0d	$$⊢\phi \to 0\le A\bar{A}$$

Proof

Step	Hyp	Ref	Expression
1		recld.1	$$⊢\phi \to A\in ℂ$$
2		cjmulge0	$$⊢A\in ℂ\to 0\le A\bar{A}$$
3	1 2	syl	$$⊢\phi \to 0\le A\bar{A}$$