let L be non empty satisfying_DN_1 ComplLattStr ; :: thesis: for x, y being Element of L holds (((x + y) ` ) + (((x ` ) + y) ` )) ` = y
let x, y be Element of L; :: thesis: (((x + y) ` ) + (((x ` ) + y) ` )) ` = y
set Z = (x + (x ` )) ` ;
(((x + y) ` ) + ((((((x + (x ` )) ` ) + x) ` ) + y) ` )) ` = y by Th5;
hence (((x + y) ` ) + (((x ` ) + y) ` )) ` = y by Th3; :: thesis: verum