Theorem absge0d

Description: Absolute value is nonnegative. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	abscld.1	$$⊢\phi \to A\in ℂ$$
Assertion	absge0d	$$⊢\phi \to 0\le \left|A\right|$$

Proof

Step	Hyp	Ref	Expression
1		abscld.1	$$⊢\phi \to A\in ℂ$$
2		absge0	$$⊢A\in ℂ\to 0\le \left|A\right|$$
3	1 2	syl	$$⊢\phi \to 0\le \left|A\right|$$