let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a 'imp' (b 'imp' c) = b 'imp' (a 'imp' c)
let a, b, c be Function of Y,BOOLEAN; :: thesis: a 'imp' (b 'imp' c) = b 'imp' (a 'imp' c)
thus a 'imp' (b 'imp' c) = ('not' a) 'or' (b 'imp' c) by BVFUNC_4:8
.= ('not' a) 'or' (('not' b) 'or' c) by BVFUNC_4:8
.= ('not' b) 'or' (('not' a) 'or' c) by BVFUNC_1:8
.= ('not' b) 'or' (a 'imp' c) by BVFUNC_4:8
.= b 'imp' (a 'imp' c) by BVFUNC_4:8 ; :: thesis: verum