let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'nand' (a 'eqv' b) = ('not' a) 'or' ('not' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a 'nand' (a 'eqv' b) = ('not' a) 'or' ('not' b)
thus a 'nand' (a 'eqv' b) = 'not' (a '&' (a 'eqv' b)) by th1
.= 'not' (a '&' ('not' (a 'xor' b))) by Th12
.= ('not' a) 'or' ('not' ('not' (a 'xor' b))) by BVFUNC_1:14
.= ('not' a) 'or' ((a 'or' b) '&' (('not' a) 'or' ('not' b))) by BVFUNC_6:86
.= (('not' a) 'or' (a 'or' b)) '&' (('not' a) 'or' (('not' a) 'or' ('not' b))) by BVFUNC_1:11
.= ((('not' a) 'or' a) 'or' b) '&' (('not' a) 'or' (('not' a) 'or' ('not' b))) by BVFUNC_1:8
.= ((I_el Y) 'or' b) '&' (('not' a) 'or' (('not' a) 'or' ('not' b))) by BVFUNC_4:6
.= (I_el Y) '&' (('not' a) 'or' (('not' a) 'or' ('not' b))) by BVFUNC_1:10
.= ('not' a) 'or' (('not' a) 'or' ('not' b)) by BVFUNC_1:6
.= (('not' a) 'or' ('not' a)) 'or' ('not' b) by BVFUNC_1:8
.= ('not' a) 'or' ('not' b) ; :: thesis: verum