Theorem abscli

Description: Real closure of absolute value. (Contributed by NM, 2-Aug-1999)

	Ref	Expression
Hypothesis	absvalsqi.1	⊢ 𝐴 ∈ ℂ
Assertion	abscli	⊢ ( abs ‘ 𝐴 ) ∈ ℝ

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	⊢ 𝐴 ∈ ℂ
2		abscl	⊢ ( 𝐴 ∈ ℂ → ( abs ‘ 𝐴 ) ∈ ℝ )
3	1 2	ax-mp	⊢ ( abs ‘ 𝐴 ) ∈ ℝ