let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds a 'imp' (a 'nand' b) = 'not' (a '&' b)
let a, b be Element of Funcs (Y,BOOLEAN); :: thesis: a 'imp' (a 'nand' b) = 'not' (a '&' b)
thus a 'imp' (a 'nand' b) = 'not' ((a '&' a) '&' b) by Th54
.= 'not' (a '&' b) ; :: thesis: verum