let R be non degenerated Ring; for V being LeftMod of R
for v1, v2 being Vector of V st {v1,v2} is linearly-independent holds
( v1 <> 0. V & v2 <> 0. V )
let V be LeftMod of R; for v1, v2 being Vector of V st {v1,v2} is linearly-independent holds
( v1 <> 0. V & v2 <> 0. V )
let v1, v2 be Vector of V; ( {v1,v2} is linearly-independent implies ( v1 <> 0. V & v2 <> 0. V ) )
A1:
( v1 in {v1,v2} & v2 in {v1,v2} )
by TARSKI:def 2;
assume
{v1,v2} is linearly-independent
; ( v1 <> 0. V & v2 <> 0. V )
hence
( v1 <> 0. V & v2 <> 0. V )
by A1, Th2; verum