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Metamath Proof Explorer

Theorem cjmulge0d

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

		Ref	Expression
	Hypothesis	recld.1	$⊢ φ \to A \in ℂ$
	Assertion	cjmulge0d	$⊢ φ \to 0 \leq A \overline{A}$

Step	Hyp	Ref	Expression
1		recld.1	$⊢ φ \to A \in ℂ$
2		cjmulge0	$⊢ A \in ℂ \to 0 \leq A \overline{A}$
3	1 2	syl	$⊢ φ \to 0 \leq A \overline{A}$