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

theorem Th75:
  for a,b,c being Function of Y,BOOLEAN holds (a 'or' b) 'imp' c =
  (a 'imp' c) '&' (b 'imp' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
    let x be Element of Y;
    ((a 'imp' c) '&' (b 'imp' c)).x =(a 'imp' c).x '&' (b 'imp' c).x by
MARGREL1:def 20
      .=('not' a.x 'or' c.x) '&' (b 'imp' c).x by BVFUNC_1:def 8
      .=(c.x 'or' 'not' a.x) '&' ('not' b.x 'or' c.x) by BVFUNC_1:def 8
      .='not'( a.x 'or' b.x) 'or' c.x by XBOOLEAN:9
      .='not' (a 'or' b).x 'or' c.x by BVFUNC_1:def 4
      .=((a 'or' b) 'imp' c).x by BVFUNC_1:def 8;
    hence thesis;
end;
