let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds
( ( a 'imp' b = I_el Y & b 'imp' a = I_el Y ) iff a = b )
let a, b be Element of Funcs (Y,BOOLEAN); :: thesis: ( ( a 'imp' b = I_el Y & b 'imp' a = I_el Y ) iff a = b )
( a 'eqv' b = I_el Y iff ( a 'imp' b = I_el Y & b 'imp' a = I_el Y ) ) by BVFUNC_4:10;
hence ( ( a 'imp' b = I_el Y & b 'imp' a = I_el Y ) iff a = b ) by BVFUNC_1:17; :: thesis: verum