let V be Z_Module; :: 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} & v2 in {v1,v2} ) by TARSKI:def 2;
assume {v1,v2} is linearly-independent ; :: thesis: v1 <> 0. V
hence v1 <> 0. V by A1, Th57; :: thesis: verum