let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN st a 'imp' c = I_el Y & b 'imp' c = I_el Y holds
(a '&' b) 'imp' c = I_el Y
let a, b, c be Function of Y,BOOLEAN; :: thesis: ( a 'imp' c = I_el Y & b 'imp' c = I_el Y implies (a '&' b) 'imp' c = I_el Y )
( a 'imp' c = I_el Y & b 'imp' c = I_el Y implies (a '&' b) 'imp' (c '&' c) = I_el Y ) by tt;
hence ( a 'imp' c = I_el Y & b 'imp' c = I_el Y implies (a '&' b) 'imp' c = I_el Y ) ; :: thesis: verum