let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs Y,BOOLEAN holds a 'nand' (b 'or' c) = ('not' (a '&' b)) '&' ('not' (a '&' c))
let a, b, c be Element of Funcs Y,BOOLEAN ; :: thesis: a 'nand' (b 'or' c) = ('not' (a '&' b)) '&' ('not' (a '&' c))
thus a 'nand' (b 'or' c) = 'not' (a '&' (b 'or' c)) by Th1
.= 'not' ((a '&' b) 'or' (a '&' c)) by BVFUNC_1:15
.= ('not' (a '&' b)) '&' ('not' (a '&' c)) by BVFUNC_1:16 ; :: thesis: verum