let L be non empty satisfying_DN_1 ComplLattStr ; :: thesis: for x, y, z being Element of L holds x + ((((y + z) ` ) + ((y + x) ` )) ` ) = ((y + x) ` ) `
let x, y, z be Element of L; :: thesis: x + ((((y + z) ` ) + ((y + x) ` )) ` ) = ((y + x) ` ) `
((x + ((((y + z) ` ) + ((y + x) ` )) ` )) ` ) ` = ((y + x) ` ) ` by Th10;
hence x + ((((y + z) ` ) + ((y + x) ` )) ` ) = ((y + x) ` ) ` by Th23; :: thesis: verum