Can a State Outlaw a City Ordinance Prohibiting LGBT Discrimination?

No federal law protects LGBT people from workplace discrimination-- but many cities have passed anti-discrimination laws to address these matters. Nashville passed such a law in 2011; however, state lawmakers essentially voided the law in "House Bill 600," which makes it illegal to enact local laws protecting LGBT people. Is this legal? More of this seems likely after the Supreme Court's marriage equality ruling. See http://www.nclrights.org/cases-and-policy/cases-and-advocacy/howe-v-haslam/ 
A ruling appears in Howe v. Haslem, here: http://scholar.google.com/scholar_case?case=16039991574862981440&q=howe+v.+haslam&hl=en&as_sdt=400006&as_vis=1