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	$$⊢\mathrm{Rel}\mathrm{NrmCVec}$$

Proof

Step	Hyp	Ref	Expression
1		nvss	$$⊢\mathrm{NrmCVec}\subseteq {CVec}_{\mathrm{OLD}}\times \mathrm{V}$$
2		relxp	$$⊢\mathrm{Rel}\left({CVec}_{\mathrm{OLD}}\times \mathrm{V}\right)$$
3		relss	$$⊢\mathrm{NrmCVec}\subseteq {CVec}_{\mathrm{OLD}}\times \mathrm{V}\to \left(\mathrm{Rel}\left({CVec}_{\mathrm{OLD}}\times \mathrm{V}\right)\to \mathrm{Rel}\mathrm{NrmCVec}\right)$$
4	1 2 3	mp2	$$⊢\mathrm{Rel}\mathrm{NrmCVec}$$