Metamath Proof Explorer


Theorem nvrel

Description: The class of all normed complex vectors spaces is a relation. (Contributed by NM, 14-Nov-2006) (New usage is discouraged.)

Ref Expression
Assertion nvrel Rel NrmCVec

Proof

Step Hyp Ref Expression
1 nvss NrmCVec ⊆ ( CVecOLD × V )
2 relxp Rel ( CVecOLD × V )
3 relss ( NrmCVec ⊆ ( CVecOLD × V ) → ( Rel ( CVecOLD × V ) → Rel NrmCVec ) )
4 1 2 3 mp2 Rel NrmCVec