theorem Th76:
  H is_subformula_of x '=' y iff H = x '=' y
proof
  thus H is_subformula_of x '=' y implies H = x '=' y
  proof
    assume
A1: H is_subformula_of x '=' y;
    assume H <> x '=' y;
    then H is_proper_subformula_of x '=' y by A1;
    then ex F st F is_immediate_constituent_of x '=' y by Th63;
    hence contradiction by Th50;
  end;
  thus thesis by Th59;
end;
