Metamath Proof Explorer


Theorem elimnv

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=BaseSetU
elimnv.5 Z=0vecU
elimnv.9 UNrmCVec
Assertion elimnv ifAXAZX

Proof

Step Hyp Ref Expression
1 elimnv.1 X=BaseSetU
2 elimnv.5 Z=0vecU
3 elimnv.9 UNrmCVec
4 1 2 nvzcl UNrmCVecZX
5 3 4 ax-mp ZX
6 5 elimel ifAXAZX