let Y be non empty set ; :: thesis: for a, b being Element of Funcs Y,BOOLEAN holds (a '&' b) 'imp' a = I_el Y
let a, b be Element of Funcs Y,BOOLEAN ; :: thesis: (a '&' b) 'imp' a = I_el Y
for x being Element of Y holds ((a '&' b) 'imp' a) . x = TRUE

proof

let x be Element of Y; :: thesis: ((a '&' b) 'imp' a) . x = TRUE
((a '&' b) 'imp' a) . x = ('not' ((a '&' b) . x)) 'or' (a . x) by BVFUNC_1:def 11
.= (('not' (a . x)) 'or' ('not' (b . x))) 'or' (a . x) by MARGREL1:def 21
.= (('not' (a . x)) 'or' (a . x)) 'or' ('not' (b . x))
.= TRUE 'or' ('not' (b . x)) by XBOOLEAN:102
.= TRUE ;
hence ((a '&' b) 'imp' a) . x = TRUE ; :: thesis: verum

end;

hence (a '&' b) 'imp' a = I_el Y by BVFUNC_1:def 14; :: thesis: verum