let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'or' (a 'nand' b) = I_el Y
let a, b be Function of Y,BOOLEAN; :: thesis: a 'or' (a 'nand' b) = I_el Y
thus a 'or' (a 'nand' b) = (a 'or' ('not' a)) 'or' ('not' b) by Th51
.= (I_el Y) 'or' ('not' b) by BVFUNC_4:6
.= I_el Y by BVFUNC_1:10 ; :: thesis: verum