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