Metamath Proof Explorer


Theorem uvccl

Description: A unit vector is a vector. (Contributed by Steven Nguyen, 16-Jul-2023)

Ref Expression
Hypotheses uvccl.u U = R unitVec I
uvccl.y Y = R freeLMod I
uvccl.b B = Base Y
Assertion uvccl R Ring I W J I U J B

Proof

Step Hyp Ref Expression
1 uvccl.u U = R unitVec I
2 uvccl.y Y = R freeLMod I
3 uvccl.b B = Base Y
4 1 2 3 uvcff R Ring I W U : I B
5 4 3adant3 R Ring I W J I U : I B
6 simp3 R Ring I W J I J I
7 5 6 ffvelrnd R Ring I W J I U J B