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 `
y ` = (y + y) ` by Th21
.= (((((x + y) ` ) + x) ` ) + y) ` by Th17 ;
hence (((((x + y) ` ) + x) ` ) + y) ` = y ` ; :: thesis: verum