let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a '&' (a 'or' b) = a

let a, b be Function of Y,BOOLEAN; :: thesis: a '&' (a 'or' b) = a

let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a '&' (a 'or' b)) . x = a . x

thus (a '&' (a 'or' b)) . x = (a . x) '&' ((a 'or' b) . x) by MARGREL1:def 20

.= (a . x) '&' ((a . x) 'or' (b . x)) by BVFUNC_1:def 4

.= a . x by XBOOLEAN:6 ; :: thesis: verum

let a, b be Function of Y,BOOLEAN; :: thesis: a '&' (a 'or' b) = a

let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a '&' (a 'or' b)) . x = a . x

thus (a '&' (a 'or' b)) . x = (a . x) '&' ((a 'or' b) . x) by MARGREL1:def 20

.= (a . x) '&' ((a . x) 'or' (b . x)) by BVFUNC_1:def 4

.= a . x by XBOOLEAN:6 ; :: thesis: verum