let I be set ; :: thesis: for M being ManySortedSet of I
for SF, SG being MSSubsetFamily of M holds SF \+\ SG is MSSubsetFamily of M
let M be ManySortedSet of I; :: thesis: for SF, SG being MSSubsetFamily of M holds SF \+\ SG is MSSubsetFamily of M
let SF, SG be MSSubsetFamily of M; :: thesis: SF \+\ SG is MSSubsetFamily of M
( SF \ SG is MSSubsetFamily of M & SG \ SF is MSSubsetFamily of M ) by Th36;
hence SF \+\ SG is MSSubsetFamily of M by Th34; :: thesis: verum