let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y, z being Element of L holds ((((((x + (y `)) + z) `) + y) `) + (((y `) + y) `)) ` = y
let x, y, z be Element of L; :: thesis: ((((((x + (y `)) + z) `) + y) `) + (((y `) + y) `)) ` = y
((x + (y `)) + y) ` = ((y `) + y) ` by Th35;
hence ((((((x + (y `)) + z) `) + y) `) + (((y `) + y) `)) ` = y by Th9; :: thesis: verum