reserve x,y,X,Y for set;
reserve C,D,E for non empty set;
reserve SC for Subset of C;
reserve SD for Subset of D;
reserve SE for Subset of E;
reserve c,c1,c2 for Element of C;
reserve d,d1,d2 for Element of D;
reserve e for Element of E;
reserve f,f1,g for PartFunc of C,D;
reserve t for PartFunc of D,C;
reserve s for PartFunc of D,E;
reserve h for PartFunc of C,E;
reserve F for PartFunc of D,D;

theorem
  dom f = {c} implies f = {[c,f/.c]}
proof
  assume dom f = {c};
  then c in dom f & f = {[c,(f qua Function).c]} by GRFUNC_1:7,TARSKI:def 1;
  hence thesis by PARTFUN1:def 6;
end;
