let GF be non empty non degenerated right_complementable well-unital distributive Abelian add-associative right_zeroed associative commutative doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for v1, v2 being Vector of V st {v1,v2} is linearly-independent holds
v1 <> 0. V
let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for v1, v2 being Vector of V st {v1,v2} is linearly-independent holds
v1 <> 0. V
let v1, v2 be Vector of V; :: thesis: ( {v1,v2} is linearly-independent implies v1 <> 0. V )
A1: v1 in {v1,v2} by TARSKI:def 2;
assume {v1,v2} is linearly-independent ; :: thesis: v1 <> 0. V
hence v1 <> 0. V by A1, Th2; :: thesis: verum