Metamath Proof Explorer

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 C_ dom adjh

Proof

Step Hyp Ref Expression
1 lncnbd 
 |-  ( LinOp i^i ContOp ) = BndLinOp
2 cnlnssadj 
 |-  ( LinOp i^i ContOp ) C_ dom adjh
3 1 2 eqsstrri 
 |-  BndLinOp C_ dom adjh