reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem Th71:
  congr b,a,p,q & congr c,a,p,r implies congr b,c,r,q
proof
  assume that
A1: congr b,a,p,q and
A2: congr c,a,p,r;
A3: congr r,p,a,c by A2,Th69;
  consider s such that
A4: congr p,q,r,s by Th63;
  congr r,p,s,q by A4,Th69;
  then
A5: congr a,c,s,q by A3,Th65;
  congr p,q,b,a by A1;
  then congr b,a,r,s by A4,Th65;
  hence thesis by A5,Th70;
end;
