let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs Y,BOOLEAN holds a 'eqv' (b 'nand' c) = (a '&' ('not' (b '&' c))) 'or' ((('not' a) '&' b) '&' c)
let a, b, c be Element of Funcs Y,BOOLEAN ; :: thesis: a 'eqv' (b 'nand' c) = (a '&' ('not' (b '&' c))) 'or' ((('not' a) '&' b) '&' c)
thus a 'eqv' (b 'nand' c) = a 'eqv' ('not' (b '&' c)) by Th1
.= (a '&' ('not' (b '&' c))) 'or' (('not' a) '&' ('not' ('not' (b '&' c)))) by BVFUNC_8:19
.= (a '&' ('not' (b '&' c))) 'or' ((('not' a) '&' b) '&' c) by BVFUNC_1:7 ; :: thesis: verum