let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y, z being Element of L holds ((((((x + y) `) + z) `) + (((x `) + y) `)) `) + y = (x `) + y
let x, y, z be Element of L; :: thesis: ((((((x + y) `) + z) `) + (((x `) + y) `)) `) + y = (x `) + y
((((((x + y) `) + z) `) + (((x `) + y) `)) `) + y = (((x `) + y) `) ` by Th47;
hence ((((((x + y) `) + z) `) + (((x `) + y) `)) `) + y = (x `) + y by Th23; :: thesis: verum