let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'eqv' (a 'nand' b) = a '&' ('not' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a 'eqv' (a 'nand' b) = a '&' ('not' b)
thus a 'eqv' (a 'nand' b) = (a '&' ('not' (a '&' b))) 'or' ((('not' a) '&' a) '&' b) by Th53
.= (a '&' ('not' (a '&' b))) 'or' ((O_el Y) '&' b) by BVFUNC_4:5
.= (a '&' ('not' (a '&' b))) 'or' (O_el Y) by BVFUNC_1:5
.= a '&' ('not' (a '&' b)) by BVFUNC_1:9
.= a '&' (('not' a) 'or' ('not' b)) by BVFUNC_1:14
.= (a '&' ('not' a)) 'or' (a '&' ('not' b)) by BVFUNC_1:12
.= (O_el Y) 'or' (a '&' ('not' b)) by BVFUNC_4:5
.= a '&' ('not' b) by BVFUNC_1:9 ; :: thesis: verum