(Adds details, background) CAIRO, May 22 (Reuters) - A bomb exploded at a Shi'ite Houthi mosque in the Yemeni capital Sanaa on Friday, wounding 13 people, a security source said, and the Islamic State claimed responsibility for the attack in a statement on Twitter. Iranian-backed Houthi rebels have seized large swathes of territory, including Sanaa, prompting formation of a Saudi-backed Arab coalition that is using air power to try to halt their advances. "Members of the caliphate in Sanaa have detonated an explosive device in a Houthi mosque in the people's district...which lead to the death and injury of many of them " said the Islamic State.