Metamath Proof Explorer


Theorem vccl

Description: Closure of the scalar product of a complex vector space. (Contributed by NM, 3-Nov-2006) (New usage is discouraged.)

Ref Expression
Hypotheses vciOLD.1 G=1stW
vciOLD.2 S=2ndW
vciOLD.3 X=ranG
Assertion vccl WCVecOLDABXASBX

Proof

Step Hyp Ref Expression
1 vciOLD.1 G=1stW
2 vciOLD.2 S=2ndW
3 vciOLD.3 X=ranG
4 1 2 3 vcsm WCVecOLDS:×XX
5 fovcdm S:×XXABXASBX
6 4 5 syl3an1 WCVecOLDABXASBX