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We report here on a local spin valve effect observed unambiguously in lateral all-semiconductor all-electrical spin injection devices, employing p+ −(Ga,Mn)As/n+ −GaAs Esaki diode structures as spin aligning contacts. We discuss the observed local spin-valve signal as a result of the interplay between spin-transport-related contribution and the tunneling anisotropic magnetoresistance of the magnetic contacts. The magnitude of the spin-related magnetoresistance change is equal to 30 Ω which is twice the magnitude of the measured non-local signal.