let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y being Element of L holds ((x + (y `)) `) + (((y `) + y) `) = (x + (y `)) `
let x, y be Element of L; :: thesis: ((x + (y `)) `) + (((y `) + y) `) = (x + (y `)) `
set X = (x + (y `)) ` ;
((x + (y `)) `) + ((((y + ((x + (y `)) `)) `) + y) `) = (x + (y `)) ` by Th28;
hence ((x + (y `)) `) + (((y `) + y) `) = (x + (y `)) ` by Th20; :: thesis: verum