let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds (a '&' b) 'imp' c = a 'imp' (('not' b) 'or' c)
let a, b, c be Function of Y,BOOLEAN; :: thesis: (a '&' b) 'imp' c = a 'imp' (('not' b) 'or' c)
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: ((a '&' b) 'imp' c) . x = (a 'imp' (('not' b) 'or' c)) . x
(a 'imp' (('not' b) 'or' c)) . x = (a 'imp' (b 'imp' c)) . x by BVFUNC_4:8;
hence ((a '&' b) 'imp' c) . x = (a 'imp' (('not' b) 'or' c)) . x by Th7; :: thesis: verum