We prove convergence of critical points to the nonlinear elastic energies J h of 3d thin incompressible plates, to critical points of the 2d energy obtained as the Γ-limit of J h in the von Kármán scaling regime. The presence of incompressibility constraint requires to restrict the class of admissible test functions to bounded divergence-free variations on the 3d deformations. This poses new technical obstacles, which we resolve by means of introducing 3d extensions and truncations of the 2d

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... iting deformations, specific to the problem at hand.