let SAS be Semi_Affine_Space; :: thesis: for p, q, r, o being Element of SAS holds p,q // sum (p,r,o), sum (q,r,o)
let p, q, r, o be Element of SAS; :: thesis: p,q // sum (p,r,o), sum (q,r,o)
congr o,p,r, sum (p,r,o) by Def5;
then A1: congr p,o, sum (p,r,o),r by Th89;
congr o,q,r, sum (q,r,o) by Def5;
hence p,q // sum (p,r,o), sum (q,r,o) by A1, Th76, Th90; :: thesis: verum