let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'nand' b = 'not' (a '&' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a 'nand' b = 'not' (a '&' b)
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a 'nand' b) . x = ('not' (a '&' b)) . x
thus ('not' (a '&' b)) . x = 'not' ((a '&' b) . x) by MARGREL1:def 19
.= 'not' ((a . x) '&' (b . x)) by MARGREL1:def 20
.= 'not' ('not' ((a . x) 'nand' (b . x))) by BVFUNC_1:46
.= (a 'nand' b) . x by Def3 ; :: thesis: verum