Theorem abscld

Description: Real closure of absolute value. (Contributed by Mario Carneiro, 29-May-2016)

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

Proof

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