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;
