reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set,
  a,b,c,d,e,f,g for Function of Y,BOOLEAN;
reserve Y for non empty set;

theorem
  for a,b,c being Function of Y,BOOLEAN holds (a 'imp' b) '&' (b
  'imp' c) '<' (a 'imp' (b 'or' 'not' c)) '&' (b 'imp' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
  (a 'imp' b) '&' (b 'imp' c) '<' (a 'imp' (b 'or' 'not' c)) by Th20;
  then
A1: (a 'imp' b) '&' (b 'imp' c) 'imp' (a 'imp' (b 'or' 'not' c))=I_el(Y) by
BVFUNC_1:16;
  (a 'imp' b) '&' (b 'imp' c) 'imp' (b 'imp' c)=I_el(Y) by Th38;
  then (a 'imp' b) '&' (b 'imp' c) 'imp' (a 'imp' (b 'or' 'not' c)) '&' (b
  'imp' c)=I_el(Y) by A1,th18;
  hence thesis by BVFUNC_1:16;
end;
