reserve L for Ortholattice,
  a, b, c for Element of L;

theorem Th5:
  for L being modular Ortholattice holds L is orthomodular
proof
  let L be modular Ortholattice;
  let x, y be Element of L;
  assume x [= y;
  then x "\/" (x` "/\" y) = (x "\/" x`) "/\" y by LATTICES:def 12;
  then x "\/" (x` "/\" y) = (y "\/" y`) "/\" y by ROBBINS3:def 7;
  hence thesis by LATTICES:def 9;
end;
