We report muon spin rotation studies of the magnetic field distribution n(B) in the vortex state of the high-temperature superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. From our data on three sets of overdoped, nearly optimized and underdoped single crystals we obtain evidence for a two-stage melting process of the vortex matter under equilibrium conditions. In the irreversible regime well below the irreversibility line we observe a transition in the vortex state which we associate with an intra-planar melting transition. The resulting flux-line liquid phase persists over a sizeable temperature interval before the inter-planar decoupling of the individual vortex lines takes place in a second step at the irreversibility line, resulting in a pancake liquid phase.
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