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Metamath Proof Explorer

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	$⊢ T \in LinOp$
	Assertion	lnopfi	$⊢ T : ℋ ⟶ ℋ$

Step	Hyp	Ref	Expression
1		lnopl.1	$⊢ T \in LinOp$
2		lnopf	$⊢ T \in LinOp \to T : ℋ ⟶ ℋ$
3	1 2	ax-mp	$⊢ T : ℋ ⟶ ℋ$