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
 for x1,x2,y being object holds
  (x1,x2) --> (y,y) = {x1,x2} --> y
proof let x1,x2,y be object;
  set F = (x1,x2)-->(y,y), f = {x1}-->y, g = {x2}-->y, F9 = {x1,x2}-->y;
  now
    thus
A1: dom F = {x1,x2} & dom F9 = {x1,x2} by Th62;
    let x be object such that
A2: x in {x1,x2};
    now
      per cases by A1,A2,Th12;
      suppose
A3:     x in dom f & not x in dom g;
        then F.x = f.x by Th11;
        hence F.x = y & F9.x = y by A2,A3,FUNCOP_1:7;
      end;
      suppose
A4:     x in dom g;
        then F.x = g.x by Th13;
        hence F.x = y & F9.x = y by A2,A4,FUNCOP_1:7;
      end;
    end;
    hence F.x = F9.x;
  end;
  hence thesis;
end;
