
theorem Th34:
  for L being satisfying_Sheffer_1 satisfying_Sheffer_2
  satisfying_Sheffer_3 properly_defined non empty ShefferOrthoLattStr holds L
  is meet-commutative
proof
  let L be satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3
  properly_defined non empty ShefferOrthoLattStr;
  let x, y be Element of L;
  x "/\" y = (x | y) | (x | y) by Def12
    .= (y | x) | (x | y) by Th31
    .= (y | x) | (y | x) by Th31
    .= y "/\" x by Def12;
  hence thesis;
end;
