Theorem hhva

Description: The group (addition) operation of Hilbert space. (Contributed by NM, 17-Nov-2007) (New usage is discouraged.)

	Ref	Expression
Hypothesis	hhnv.1	$$⊢U=⟨⟨{+}_{ℎ},{\cdot }_{ℎ}⟩,{norm}_{ℎ}⟩$$
Assertion	hhva	$$⊢{+}_{ℎ}={+}_v\left(U\right)$$

Proof

Step	Hyp	Ref	Expression
1		hhnv.1	$$⊢U=⟨⟨{+}_{ℎ},{\cdot }_{ℎ}⟩,{norm}_{ℎ}⟩$$
2	1	hhnv	$$⊢U\in \mathrm{NrmCVec}$$
3	1 2	h2hva	$$⊢{+}_{ℎ}={+}_v\left(U\right)$$