let Y be non empty set ; :: thesis: for a, b being Element of Funcs Y,BOOLEAN holds a 'nand' (a 'nor' b) = I_el Y
let a, b be Element of Funcs Y,BOOLEAN ; :: thesis: a 'nand' (a 'nor' b) = I_el Y
thus a 'nand' (a 'nor' b) = 'not' (a '&' (a 'nor' b)) by Th1
.= 'not' (a '&' ('not' (a 'or' b))) by Th2
.= ('not' a) 'or' ('not' ('not' (a 'or' b))) by BVFUNC_1:17
.= (('not' a) 'or' a) 'or' b by BVFUNC_1:11
.= (I_el Y) 'or' b by BVFUNC_4:6
.= I_el Y by BVFUNC_1:13 ; :: thesis: verum