let F be Field; :: thesis: for S being SymSp of F
for b, a, x, y being Element of S st (1_ F) + (1_ F) <> 0. F & not a _|_ & x = 0. S holds
PProJ a,b,x,y = 0. F
let S be SymSp of F; :: thesis: for b, a, x, y being Element of S st (1_ F) + (1_ F) <> 0. F & not a _|_ & x = 0. S holds
PProJ a,b,x,y = 0. F
let b, a, x, y be Element of S; :: thesis: ( (1_ F) + (1_ F) <> 0. F & not a _|_ & x = 0. S implies PProJ a,b,x,y = 0. F )
assume that
A1: (1_ F) + (1_ F) <> 0. F and
A2: ( not a _|_ & x = 0. S ) ; :: thesis: PProJ a,b,x,y = 0. F
for p being Element of S holds
( a _|_ or x _|_ ) by A2, Th11, Th12;
hence PProJ a,b,x,y = 0. F by A1, A2, Def6; :: thesis: verum