let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds a 'imp' (O_el Y) = 'not' a
let a be Function of Y,BOOLEAN; :: thesis: a 'imp' (O_el Y) = 'not' a
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: K11((a 'imp' (O_el Y)),x) = K11(('not' a),x)
(a 'imp' (O_el Y)) . x = ('not' (a . x)) 'or' ((O_el Y) . x) by BVFUNC_1:def 8
.= ('not' (a . x)) 'or' FALSE by BVFUNC_1:def 10
.= 'not' (a . x) ;
hence K11((a 'imp' (O_el Y)),x) = K11(('not' a),x) by MARGREL1:def 19; :: thesis: verum