Metamath Proof Explorer


Theorem lbsel

Description: An element of a basis is a vector. (Contributed by Mario Carneiro, 24-Jun-2014)

Ref Expression
Hypotheses lbsss.v 𝑉 = ( Base ‘ 𝑊 )
lbsss.j 𝐽 = ( LBasis ‘ 𝑊 )
Assertion lbsel ( ( 𝐵𝐽𝐸𝐵 ) → 𝐸𝑉 )

Proof

Step Hyp Ref Expression
1 lbsss.v 𝑉 = ( Base ‘ 𝑊 )
2 lbsss.j 𝐽 = ( LBasis ‘ 𝑊 )
3 1 2 lbsss ( 𝐵𝐽𝐵𝑉 )
4 3 sselda ( ( 𝐵𝐽𝐸𝐵 ) → 𝐸𝑉 )