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;

theorem
  (a 'or' b) 'imp' c '<' a 'imp' c
proof
  let z be Element of Y;
A1: ((a 'or' b) 'imp' c).z =('not'( a 'or' b) 'or' c).z by BVFUNC_4:8
    .=(('not' a '&' 'not' b) 'or' c).z by BVFUNC_1:13
    .=('not' a '&' 'not' b).z 'or' c.z by BVFUNC_1:def 4
    .=(('not' a).z '&' ('not' b).z) 'or' c.z by MARGREL1:def 20;
  assume
A2: ((a 'or' b) 'imp' c).z=TRUE;
  now
    assume (a 'imp' c).z<>TRUE;
    then (a 'imp' c).z=FALSE by XBOOLEAN:def 3;
    then ('not' a 'or' c).z=FALSE by BVFUNC_4:8;
    then
A3: ('not' a).z 'or' c.z=FALSE by BVFUNC_1:def 4;
    (('not' a).z '&' ('not' b).z) 'or' c.z =(c.z 'or' ('not' a).z) '&' (c.
    z 'or' ('not' b).z) by XBOOLEAN:9
      .=FALSE by A3;
    hence contradiction by A2,A1;
  end;
  hence thesis;
end;
