reserve x,y for set;
reserve X for non empty set;
reserve a,b,c,d for Element of X;
reserve S for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u,w for Element of S;

theorem Th3:
  z<>t & x,y // z,t & z,t // u,w implies x,y // u,w
proof
  assume
A1: z<>t;
  assume that
A2: x,y // z,t and
A3: z,t // u,w;
  z,t // x,y by A2,Th2;
  hence thesis by A1,A3,ANALOAF:def 5;
end;
