let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs Y,BOOLEAN holds a 'imp' (b 'nand' c) = 'not' ((a '&' b) '&' c)
let a, b, c be Element of Funcs Y,BOOLEAN ; :: thesis: a 'imp' (b 'nand' c) = 'not' ((a '&' b) '&' c)
thus a 'imp' (b 'nand' c) = a 'imp' ('not' (b '&' c)) by Th1
.= ('not' a) 'or' ('not' (b '&' c)) by BVFUNC_4:8
.= 'not' (a '&' (b '&' c)) by BVFUNC_1:17
.= 'not' ((a '&' b) '&' c) by BVFUNC_1:7 ; :: thesis: verum