let Y be non empty set ; :: thesis: for a, b being Element of Funcs Y,BOOLEAN holds a 'imp' b = ('not' a) 'or' b
let a, b be Element of Funcs Y,BOOLEAN ; :: thesis: a 'imp' b = ('not' a) 'or' b
A1: for x being Element of Y holds (a 'imp' b) . x = (('not' a) 'or' b) . x

proof

let x be Element of Y; :: thesis: (a 'imp' b) . x = (('not' a) 'or' b) . x
(a 'imp' b) . x = ('not' (a . x)) 'or' (b . x) by BVFUNC_1:def 11
.= (('not' a) . x) 'or' (b . x) by MARGREL1:def 20
.= (('not' a) 'or' b) . x by BVFUNC_1:def 7 ;
hence (a 'imp' b) . x = (('not' a) 'or' b) . x ; :: thesis: verum

end;

consider k3 being Function such that
A2: ( a 'imp' b = k3 & dom k3 = Y & rng k3 c= BOOLEAN ) by FUNCT_2:def 2;
consider k4 being Function such that
A3: ( ('not' a) 'or' b = k4 & dom k4 = Y & rng k4 c= BOOLEAN ) by FUNCT_2:def 2;
for u being set st u in Y holds
k3 . u = k4 . u by A1, A2, A3;
hence a 'imp' b = ('not' a) 'or' b by A2, A3, FUNCT_1:9; :: thesis: verum