let L be non empty satisfying_DN_1 ComplLattStr ; :: thesis: for x, y, z being Element of L holds ((((x + y) ` ) + (x + z)) ` ) + y = y
let x, y, z be Element of L; :: thesis: ((((x + y) ` ) + (x + z)) ` ) + y = y
(((x + y) ` ) + ((((x + y) ` ) + ((x + z) ` )) ` )) ` = (((x + y) ` ) + (x + z)) ` by Th45;
hence ((((x + y) ` ) + (x + z)) ` ) + y = y by Th40; :: thesis: verum