Description: Hypothesis elimination lemma for complex inner product spaces to assist weak deduction theorem. (Contributed by NM, 27-Apr-2007) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | elimph.1 | |- X = ( BaseSet ` U ) |
|
| elimph.5 | |- Z = ( 0vec ` U ) |
||
| elimph.6 | |- U e. CPreHilOLD |
||
| Assertion | elimph | |- if ( A e. X , A , Z ) e. X |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elimph.1 | |- X = ( BaseSet ` U ) |
|
| 2 | elimph.5 | |- Z = ( 0vec ` U ) |
|
| 3 | elimph.6 | |- U e. CPreHilOLD |
|
| 4 | 3 | phnvi | |- U e. NrmCVec |
| 5 | 1 2 4 | elimnv | |- if ( A e. X , A , Z ) e. X |