let FCPS be up-3-dimensional CollProjectiveSpace; :: thesis: for a, b, c, b' being Element of FCPS st not a,b,c is_collinear & a,b,b' is_collinear & a <> b' holds
not a,b',c is_collinear
let a, b, c, b' be Element of FCPS; :: thesis: ( not a,b,c is_collinear & a,b,b' is_collinear & a <> b' implies not a,b',c is_collinear )
assume A1: ( not a,b,c is_collinear & a,b,b' is_collinear & a <> b' ) ; :: thesis: not a,b',c is_collinear
assume a,b',c is_collinear ; :: thesis: contradiction
then ( a,b',b is_collinear & a,b',c is_collinear ) by A1, Th1;
hence contradiction by A1, COLLSP:11; :: thesis: verum