Theorem bdopssadj

Description: Every bounded linear Hilbert space operator has an adjoint. (Contributed by NM, 19-Feb-2006) (New usage is discouraged.)

	Ref	Expression
Assertion	bdopssadj	⊢ BndLinOp ⊆ dom adjℎ

Proof

Step	Hyp	Ref	Expression
1		lncnbd	⊢ ( LinOp ∩ ContOp ) = BndLinOp
2		cnlnssadj	⊢ ( LinOp ∩ ContOp ) ⊆ dom adjℎ
3	1 2	eqsstrri	⊢ BndLinOp ⊆ dom adjℎ