let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds (b 'imp' c) 'imp' ((a '&' b) 'imp' c) = I_el Y
let a, b, c be Function of Y,BOOLEAN; :: thesis: (b 'imp' c) 'imp' ((a '&' b) 'imp' c) = I_el Y
thus (b 'imp' c) 'imp' ((a '&' b) 'imp' c) = ('not' (b 'imp' c)) 'or' ((a '&' b) 'imp' c) by BVFUNC_4:8
.= ('not' (('not' b) 'or' c)) 'or' ((a '&' b) 'imp' c) by BVFUNC_4:8
.= ('not' (('not' b) 'or' c)) 'or' (('not' (a '&' b)) 'or' c) by BVFUNC_4:8
.= (('not' ('not' b)) '&' ('not' c)) 'or' (('not' (a '&' b)) 'or' c) by BVFUNC_1:13
.= (b '&' ('not' c)) 'or' ((('not' a) 'or' ('not' b)) 'or' c) by BVFUNC_1:14
.= ((b '&' ('not' c)) 'or' c) 'or' (('not' a) 'or' ('not' b)) by BVFUNC_1:8
.= ((b 'or' c) '&' (('not' c) 'or' c)) 'or' (('not' a) 'or' ('not' b)) by BVFUNC_1:11
.= ((b 'or' c) '&' (I_el Y)) 'or' (('not' a) 'or' ('not' b)) by BVFUNC_4:6
.= (('not' a) 'or' ('not' b)) 'or' (b 'or' c) by BVFUNC_1:6
.= ((('not' a) 'or' ('not' b)) 'or' b) 'or' c by BVFUNC_1:8
.= (('not' a) 'or' (('not' b) 'or' b)) 'or' c by BVFUNC_1:8
.= (('not' a) 'or' (I_el Y)) 'or' c by BVFUNC_4:6
.= (I_el Y) 'or' c by BVFUNC_1:10
.= I_el Y by BVFUNC_1:10 ; :: thesis: verum