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Metamath Proof Explorer
Description: Composition with the Hilbert space identity operator. (Contributed by NM, 24-Aug-2006) (New usage is discouraged.)
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|
Ref |
Expression |
|
Assertion |
hoico1 |
⊢ ( 𝑇 : ℋ ⟶ ℋ → ( 𝑇 ∘ Iop ) = 𝑇 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
dfiop2 |
⊢ Iop = ( I ↾ ℋ ) |
| 2 |
1
|
coeq2i |
⊢ ( 𝑇 ∘ Iop ) = ( 𝑇 ∘ ( I ↾ ℋ ) ) |
| 3 |
|
fcoi1 |
⊢ ( 𝑇 : ℋ ⟶ ℋ → ( 𝑇 ∘ ( I ↾ ℋ ) ) = 𝑇 ) |
| 4 |
2 3
|
eqtrid |
⊢ ( 𝑇 : ℋ ⟶ ℋ → ( 𝑇 ∘ Iop ) = 𝑇 ) |