reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;
reserve A,B for non empty set;
reserve Y for non empty set,
  f for Function of X,Y,
  p for PartFunc of Y,Z,
  x for Element of X;

theorem Th108:
  X <> {} & rng f c= dom p implies (p/*f).x = p/.(f.x)
proof
  assume that
A1: X <> {} and
A2: rng f c= dom p;
A3: f.x in rng f by A1,Th4;
  thus (p/*f).x = p.(f.x) by A1,A2,Th107
    .= p/.(f.x) by A2,A3,PARTFUN1:def 6;
end;
