Theorem normcli

Description: Real closure of the norm of a vector. (Contributed by NM, 30-Sep-1999) (New usage is discouraged.)

	Ref	Expression
Hypothesis	normcl.1	⊢ 𝐴 ∈ ℋ
Assertion	normcli	⊢ ( normℎ ‘ 𝐴 ) ∈ ℝ

Proof

Step	Hyp	Ref	Expression
1		normcl.1	⊢ 𝐴 ∈ ℋ
2		normcl	⊢ ( 𝐴 ∈ ℋ → ( normℎ ‘ 𝐴 ) ∈ ℝ )
3	1 2	ax-mp	⊢ ( normℎ ‘ 𝐴 ) ∈ ℝ