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Metamath Proof Explorer

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