Dialectical Materialism and Master-Slave Dialectic

While Marx presents Dialectical Materialism as an inversion of Hegel's Dialectical Idealism, textual evidence strongly suggests that it is actually already a moment in the latter.  For, in the passage of Phenomenology of Mind usually referred to as the 'Master-Slave Dialectic', the Slave achieves liberation from the Master through Labor, in which he arrives at Self-Consciousness, constituted by the recognition of himself in his Labor.  In turn, Hegel, in that passage, is likely influenced by Kant's 'Refutation of Idealism', from the second edition of the 1st Critique, in which "the game played by idealism has been turned against itself, and with greater justice", as Kant puts it in B276. Furthermore, this modification of the first edition reflects the incorporation of Rousseau's General Will into Kant's system, specifically in the establishment of the priority of Practice over Theory, a transformation that also includes Kant's acknowledgement of kinship with the 'Copernican Revolution',  So, Marx only assumes the already established inversion, with his novel contribution to the tradition being its application to Capitalism, in particular.