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;
reserve A,B for set;
reserve x,y,i,j,k for object;

theorem
  for a,b,c,d being set, f being Function st
  a in dom f & c in dom f & f.a = b & f.c = d holds (a,c) --> (b,d) c= f
proof
  let a,b,c,d be set, f be Function;
  assume that
A1: a in dom f and
A2: c in dom f and
A3: f.a = b & f.c = d;
  per cases;
  suppose
A4: a <> c;
    [a,b] in f & [c,d] in f by A1,A2,A3,FUNCT_1:1;
    then { [a,b], [c,d]} c= f by ZFMISC_1:32;
    hence thesis by A4,Th67;
  end;
  suppose
    a = c;
    hence thesis by A1,A3,Th85;
  end;
end;
