Description: Hilbert space scalar multiplication by one. (Contributed by NM, 7-Sep-2007) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hlmulf.1 | |- X = ( BaseSet ` U ) |
|
hlmulf.4 | |- S = ( .sOLD ` U ) |
||
Assertion | hlmulid | |- ( ( U e. CHilOLD /\ A e. X ) -> ( 1 S A ) = A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hlmulf.1 | |- X = ( BaseSet ` U ) |
|
2 | hlmulf.4 | |- S = ( .sOLD ` U ) |
|
3 | hlnv | |- ( U e. CHilOLD -> U e. NrmCVec ) |
|
4 | 1 2 | nvsid | |- ( ( U e. NrmCVec /\ A e. X ) -> ( 1 S A ) = A ) |
5 | 3 4 | sylan | |- ( ( U e. CHilOLD /\ A e. X ) -> ( 1 S A ) = A ) |