Metamath Proof Explorer


Theorem elimnvu

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

Proof

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