let SAS be Semi_Affine_Space; :: thesis: for a, b, c, p, r being Element of SAS st not a,b // a,c & a,c // p,r & b,c // p,r holds
p = r
let a, b, c, p, r be Element of SAS; :: thesis: ( not a,b // a,c & a,c // p,r & b,c // p,r implies p = r )
assume that
A1: ( not a,b // a,c & a,c // p,r ) and
A2: b,c // p,r ; :: thesis: p = r
A3: p,r // b,c by A2, Th6;
( not a,c // b,c & p,r // a,c ) by A1, Th6, Th14;
hence p = r by A3, Def1; :: thesis: verum