reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem Th15:
  x in dom g & h = f \/ g implies h.x = g.x
proof
  assume x in dom g;
  then [x,g.x] in g by FUNCT_1:def 2;
  then h = f \/ g implies [x,g.x] in h by XBOOLE_0:def 3;
  hence thesis by FUNCT_1:1;
end;
