Metamath Proof Explorer


Theorem hhxmet

Description: The induced metric of Hilbert space. (Contributed by Mario Carneiro, 10-Sep-2015) (New usage is discouraged.)

Ref Expression
Hypotheses hhnv.1 U = + norm
hhims2.2 D = IndMet U
Assertion hhxmet D ∞Met

Proof

Step Hyp Ref Expression
1 hhnv.1 U = + norm
2 hhims2.2 D = IndMet U
3 1 2 hhmet D Met
4 metxmet D Met D ∞Met
5 3 4 ax-mp D ∞Met