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Metamath Proof Explorer

Theorem hoival

Description: The value of the Hilbert space identity operator. (Contributed by NM, 8-Aug-2006) (New usage is discouraged.)

		Ref	Expression
	Assertion	hoival	$⊢ A \in ℋ \to I_{op} (A) = A$

Step	Hyp	Ref	Expression
1		df-iop	$⊢ I_{op} = {proj}_{ℎ} (ℋ)$
2	1	fveq1i	$⊢ I_{op} (A) = {proj}_{ℎ} (ℋ) (A)$
3		pjch1	$⊢ A \in ℋ \to {proj}_{ℎ} (ℋ) (A) = A$
4	2 3	eqtrid	$⊢ A \in ℋ \to I_{op} (A) = A$