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
let x, y, z be Element of L; :: thesis: (((x + y) `) + ((((z + x) `) + y) `)) ` = y
set u = the Element of L;
set U = ((y `) + ((y + the Element of L) `)) ` ;
(((x + y) `) + ((((z + x) `) + ((((((y + (y `)) `) + y) `) + ((y + (((y `) + ((y + the Element of L) `)) `)) `)) `)) `)) ` = y by Th4;
hence (((x + y) `) + ((((z + x) `) + y) `)) ` = y by Def1; :: thesis: verum