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

theorem Th76:
  for a,b,c being Function of Y,BOOLEAN holds (a '&' b) 'imp' c =
  (a 'imp' c) 'or' (b 'imp' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
    let x be Element of Y;
    ((a 'imp' c) 'or' (b 'imp' c)).x =(a 'imp' c).x 'or' (b 'imp' c).x by
BVFUNC_1:def 4
      .=('not' a.x 'or' c.x) 'or' (b 'imp' c).x by BVFUNC_1:def 8
      .=('not' a.x 'or' c.x) 'or' ('not' b.x 'or' c.x) by
BVFUNC_1:def 8
      .=('not' a.x 'or' (c.x 'or' 'not' b.x)) 'or' c.x 
      .=(('not' a.x 'or' 'not' b.x) 'or' c.x) 'or' c.x 
      .=('not' a.x 'or' 'not' b.x) 'or' (c.x 'or' c.x) by BINARITH:11
      .='not' (a '&' b).x 'or' c.x by MARGREL1:def 20
      .=((a '&' b) 'imp' c).x by BVFUNC_1:def 8;
    hence thesis;
end;
