let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'imp' ((a 'imp' b) 'imp' a) = I_el Y
let a, b be Function of Y,BOOLEAN; :: thesis: a 'imp' ((a 'imp' b) 'imp' a) = I_el Y
thus a 'imp' ((a 'imp' b) 'imp' a) = ('not' a) 'or' ((a 'imp' b) 'imp' a) by BVFUNC_4:8
.= ('not' a) 'or' (('not' (a 'imp' b)) 'or' a) by BVFUNC_4:8
.= ('not' a) 'or' (('not' (('not' a) 'or' b)) 'or' a) by BVFUNC_4:8
.= ('not' a) 'or' ((('not' ('not' a)) '&' ('not' b)) 'or' a) by BVFUNC_1:13
.= (('not' a) 'or' a) 'or' (a '&' ('not' b)) by BVFUNC_1:8
.= (I_el Y) 'or' (a '&' ('not' b)) by BVFUNC_4:6
.= I_el Y by BVFUNC_1:10 ; :: thesis: verum