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 )