let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'imp' b = ('not' a) 'or' b
let a, b be Function of Y,BOOLEAN; :: thesis: a 'imp' b = ('not' a) 'or' b
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a 'imp' b) . x = (('not' a) 'or' b) . x
thus (a 'imp' b) . x = (a . x) => (b . x) by BVFUNC_1:def 8
.= ('not' (a . x)) 'or' (b . x)
.= (('not' a) . x) 'or' (b . x) by MARGREL1:def 19
.= (('not' a) 'or' b) . x by BVFUNC_1:def 4 ; :: thesis: verum