let SAS be Semi_Affine_Space; 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; ( 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
; 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; verum