Theorem abscld

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

	Ref	Expression
Hypothesis	abscld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	abscld	⊢ ( 𝜑 → ( abs ‘ 𝐴 ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		abscld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		abscl	⊢ ( 𝐴 ∈ ℂ → ( abs ‘ 𝐴 ) ∈ ℝ )
3	1 2	syl	⊢ ( 𝜑 → ( abs ‘ 𝐴 ) ∈ ℝ )