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Metamath Proof Explorer

Theorem lnop0i

Description: The value of a linear Hilbert space operator at zero is zero. Remark in Beran p. 99. (Contributed by NM, 11-May-2005) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	lnopl.1	$⊢ T \in LinOp$
	Assertion	lnop0i	$⊢ T (0_{ℎ}) = 0_{ℎ}$

Proof

Step	Hyp	Ref	Expression
1		lnopl.1	$⊢ T \in LinOp$
2		lnop0	$⊢ T \in LinOp \to T (0_{ℎ}) = 0_{ℎ}$
3	1 2	ax-mp	$⊢ T (0_{ℎ}) = 0_{ℎ}$