Metamath Proof Explorer


Theorem nmcvfval

Description: Value of the norm function in a normed complex vector space. (Contributed by NM, 25-Apr-2007) (New usage is discouraged.)

Ref Expression
Hypothesis nmfval.6 ⊢ N = norm CV ⁡ U
Assertion nmcvfval ⊢ N = 2 nd ⁡ U

Proof

Step Hyp Ref Expression
1 nmfval.6 ⊢ N = norm CV ⁡ U
2 df-nmcv ⊢ norm CV = 2 nd
3 2 fveq1i ⊢ norm CV ⁡ U = 2 nd ⁡ U
4 1 3 eqtri ⊢ N = 2 nd ⁡ U