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Metamath Proof Explorer

Theorem hoico2

Description: Composition with the Hilbert space identity operator. (Contributed by NM, 24-Aug-2006) (New usage is discouraged.)

		Ref	Expression
	Assertion	hoico2	$⊢ T : ℋ ⟶ ℋ \to I_{op} \circ T = T$

Step	Hyp	Ref	Expression
1		dfiop2	$⊢ I_{op} = {I ↾}_{ℋ}$
2	1	coeq1i	$⊢ I_{op} \circ T = ({I ↾}_{ℋ}) \circ T$
3		fcoi2	$⊢ T : ℋ ⟶ ℋ \to ({I ↾}_{ℋ}) \circ T = T$
4	2 3	eqtrid	$⊢ T : ℋ ⟶ ℋ \to I_{op} \circ T = T$