theorem Th51: :: EC_PF_2:51

for p being 5 _or_greater Prime
for z being Element of EC_WParam p
for P, Q being Element of EC_SetProjCo ((z `1),(z `2),p) st P `3_3 <> 0 & Q `3_3 <> 0 & P `2_3 <> 0 & P _EQ_ (compell_ProjCo (z,p)) . Q holds
(P `2_3) * (Q `3_3) <> (Q `2_3) * (P `3_3)