Theorem lnopfi

Description: A linear Hilbert space operator is a Hilbert space operator. (Contributed by NM, 23-Jan-2006) (New usage is discouraged.)

	Ref	Expression
Hypothesis	lnopl.1	⊢ 𝑇 ∈ LinOp
Assertion	lnopfi	⊢ 𝑇 : ℋ ⟶ ℋ

Proof

Step	Hyp	Ref	Expression
1		lnopl.1	⊢ 𝑇 ∈ LinOp
2		lnopf	⊢ ( 𝑇 ∈ LinOp → 𝑇 : ℋ ⟶ ℋ )
3	1 2	ax-mp	⊢ 𝑇 : ℋ ⟶ ℋ