  We demonstrate how to efficiently derive a broad class of inequalities for
entanglement detection in multi-mode continuous variable systems. The
separability conditions are established from partial transposition (PT) in
combination with several distinct necessary conditions for a quantum physical
state, which include previously established inequalities as special cases.
Remarkably, our method enables us to support Peres' conjecture to its full
generality within the framework of Cavalcanti-Foster-Reid-Drummond multipartite
Bell inequality [Phys. Rev. Lett. 99}, 210405 (2007)] that the nonlocality
necessarily implies negative PT entangled states.
