The ground state of Li-11 is the preeminent example of a two-neutron-halo nucleus and is part of an isobaric sextet. Another member of this sextet, the double isobaric analog of Li-11(g.s). in B-11, has been identified in the Be-12(p, 2n)B-11 reaction. The state was discovered through its two-proton decay branch. From detected 2p + Li-9 events, its excitation energy was determined to be 33.57(8) MeV using the invariant mass method. With the known masses of Li-11 and its isobaric analog state in Be-11, three members of the same sextet have measured masses for the first time, permitting the masses of the remaining members to be extrapolated using the isobaric multiplet mass equation. All members of this multiplet are expected to have a two-nucleon halo structure and this was found consistent with the evolution of the mass across the sextet. The momentum correlations of the detected protons were found to have both "diproton" and "cigar" components.