reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem Th5:
 for a,b being object holds
  X --> a c= Y --> b implies X c= Y
proof let a,b be object;
  assume X --> a c= Y --> b;
  then
A1: dom(X --> a) c= dom(Y --> b) by RELAT_1:11;
  thus thesis by A1;
end;
