reserve Y for non empty set;
reserve Y for non empty set;

theorem Th73:
  for a,b,c being Function of Y,BOOLEAN holds a 'imp' (b 'or' c) =
  (a 'imp' b) 'or' (a 'imp' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
    let x be Element of Y;
    ((a 'imp' b) 'or' (a 'imp' c)).x =(a 'imp' b).x 'or' (a 'imp' c).x by
BVFUNC_1:def 4
      .=('not' a.x 'or' b.x) 'or' (a 'imp' c).x by BVFUNC_1:def 8
      .=('not' a.x 'or' b.x) 'or' ('not' a.x 'or' c.x) by
BVFUNC_1:def 8
      .=('not' a.x 'or' ('not' a.x 'or' b.x)) 'or' c.x
      .=(('not' a.x 'or' 'not' a.x) 'or' b.x) 'or' c.x by BINARITH:11
      .='not' a.x 'or' (b.x 'or' c.x)
      .='not' a.x 'or' (b 'or' c).x by BVFUNC_1:def 4
      .=(a 'imp' (b 'or' c)).x by BVFUNC_1:def 8;
    hence thesis;
end;
