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 Th67:
  congr a,b,c,d implies congr b,a,d,c
proof
  assume
A1: congr a,b,c,d;
A2: now
    assume a<>b;
    then consider p,q such that
A3: parallelogram p,q,a,b & parallelogram p, q,c,d by A1;
    parallelogram q,p,b,a & parallelogram q,p,d,c by A3,Th43;
    hence thesis;
  end;
  a=b implies thesis by A1,Th54;
  hence thesis by A2;
end;
