let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs Y,BOOLEAN holds a 'nor' (b 'imp' c) = (('not' a) '&' b) '&' ('not' c)
let a, b, c be Element of Funcs Y,BOOLEAN ; :: thesis: a 'nor' (b 'imp' c) = (('not' a) '&' b) '&' ('not' c)
thus a 'nor' (b 'imp' c) = 'not' (a 'or' (b 'imp' c)) by Th2
.= ('not' a) '&' ('not' (b 'imp' c)) by BVFUNC_1:16
.= ('not' a) '&' (b '&' ('not' c)) by BVFUNC25:1
.= (('not' a) '&' b) '&' ('not' c) by BVFUNC_1:7 ; :: thesis: verum