Theorem absnegd

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

	Ref	Expression
Hypothesis	abscld.1	$$⊢\phi \to A\in ℂ$$
Assertion	absnegd	$$⊢\phi \to \left|-A\right|=\left|A\right|$$

Proof

Step	Hyp	Ref	Expression
1		abscld.1	$$⊢\phi \to A\in ℂ$$
2		absneg	$$⊢A\in ℂ\to \left|-A\right|=\left|A\right|$$
3	1 2	syl	$$⊢\phi \to \left|-A\right|=\left|A\right|$$