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 | ||
|---|---|---|---|
| Assertion | elimnvu | |- if ( U e. NrmCVec , U , <. <. + , x. >. , abs >. ) e. NrmCVec |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqid | |- <. <. + , x. >. , abs >. = <. <. + , x. >. , abs >. |
|
| 2 | 1 | cnnv | |- <. <. + , x. >. , abs >. e. NrmCVec |
| 3 | 2 | elimel | |- if ( U e. NrmCVec , U , <. <. + , x. >. , abs >. ) e. NrmCVec |