Metamath Proof Explorer


Theorem bdopadj

Description: Every bounded linear Hilbert space operator has an adjoint. (Contributed by NM, 22-Feb-2006) (New usage is discouraged.)

Ref Expression
Assertion bdopadj ( 𝑇 ∈ BndLinOp → 𝑇 ∈ dom adjℎ )

Proof

Step Hyp Ref Expression
1 bdopssadj ⊢ BndLinOp ⊆ dom adjℎ
2 1 sseli ⊢ ( 𝑇 ∈ BndLinOp → 𝑇 ∈ dom adjℎ )