reserve n for Element of NAT,
  p,q,r,s for Element of HP-WFF;

theorem Th9:
  for a,b,x,y,x9,y9 being set st a <> b &
  (a,b) --> (x,y) = (a,b) --> (x9,y9) holds x = x9 & y = y9
proof
  let a,b,x,y,x9,y9 be set such that
A1: a <> b and
A2: (a,b) --> (x,y) = (a,b) --> (x9,y9);
  thus x = ((a,b) --> (x,y)).a by A1,FUNCT_4:63
    .= x9 by A1,A2,FUNCT_4:63;
  thus y = ((a,b) --> (x,y)).b by FUNCT_4:63
    .= y9 by A2,FUNCT_4:63;
end;
