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	$$⊢T\in \mathrm{BndLinOp}\to T\in \mathrm{dom}{adj}_h$$

Proof

Step	Hyp	Ref	Expression
1		bdopssadj	$$⊢\mathrm{BndLinOp}\subseteq \mathrm{dom}{adj}_h$$
2	1	sseli	$$⊢T\in \mathrm{BndLinOp}\to T\in \mathrm{dom}{adj}_h$$