let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs (Y,BOOLEAN) holds a 'or' (b 'nand' c) = (a 'or' ('not' b)) 'or' ('not' c)
let a, b, c be Element of Funcs (Y,BOOLEAN); :: thesis: a 'or' (b 'nand' c) = (a 'or' ('not' b)) 'or' ('not' c)
thus a 'or' (b 'nand' c) = a 'or' ('not' (b '&' c)) by Th1
.= a 'or' (('not' b) 'or' ('not' c)) by BVFUNC_1:14
.= (a 'or' ('not' b)) 'or' ('not' c) by BVFUNC_1:8 ; :: thesis: verum