let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds a 'or' (O_el Y) = a
let a be Function of Y,BOOLEAN; :: thesis: a 'or' (O_el Y) = a
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a 'or' (O_el Y)) . x = a . x
thus (a 'or' (O_el Y)) . x = (a . x) 'or' ((O_el Y) . x) by Def4
.= (a . x) 'or' FALSE by Def10
.= a . x ; :: thesis: verum