Description: Hypothesis elimination lemma for normed complex vector spaces to assist weak deduction theorem. (Contributed by NM, 16-May-2007) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | elimnv.1 | |- X = ( BaseSet ` U ) |
|
elimnv.5 | |- Z = ( 0vec ` U ) |
||
elimnv.9 | |- U e. NrmCVec |
||
Assertion | elimnv | |- if ( A e. X , A , Z ) e. X |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elimnv.1 | |- X = ( BaseSet ` U ) |
|
2 | elimnv.5 | |- Z = ( 0vec ` U ) |
|
3 | elimnv.9 | |- U e. NrmCVec |
|
4 | 1 2 | nvzcl | |- ( U e. NrmCVec -> Z e. X ) |
5 | 3 4 | ax-mp | |- Z e. X |
6 | 5 | elimel | |- if ( A e. X , A , Z ) e. X |