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Metamath Proof Explorer

Theorem cjmulge0i

Description: A complex number times its conjugate is nonnegative. (Contributed by NM, 28-May-1999)

		Ref	Expression
	Hypothesis	recl.1	$⊢ A \in ℂ$
	Assertion	cjmulge0i	$⊢ 0 \leq A \overline{A}$

Step	Hyp	Ref	Expression
1		recl.1	$⊢ A \in ℂ$
2		cjmulge0	$⊢ A \in ℂ \to 0 \leq A \overline{A}$
3	1 2	ax-mp	$⊢ 0 \leq A \overline{A}$