let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: L is join-commutative

for x, y being Element of L holds x + y = y + x by Th27;

hence L is join-commutative by LATTICES:def 4; :: thesis: verum

for x, y being Element of L holds x + y = y + x by Th27;

hence L is join-commutative by LATTICES:def 4; :: thesis: verum