Proletariat, Property, Labor

One elucidation by Marx of the emergence of Socialism is: 1. The Proletariat is the revolutionary Class; 2. The principles of any ruling Class are expressions of its fundamental characteristics; 3.  The fundamental characteristic of the Proletariat is property-lessness; 4. Thus, the defining characteristic of an ascendant Proletariat is property-lessness;  5. The fundamental characteristic of Socialism is the abolition of Private Property; 6. Thus, Socialism is the result of a Proletariat revolution.  Now, #3 is problematic, because it assumes that the Proletariat remains property-less after a revolution, i. e. that its members do not keep what they have seized for themselves.  But, the deeper problem with that premise is that it is false.  For, it is a cardinal tenet of Marxism that any worker owns their Labor, as well as the fruits of it, even as it is alienated from them.  Thus, the Proletariat is not property-less, with, therefore, 4. Thus, the defining characteristic of an ascendant Proletariat is Labor.  Accordingly, #6 can be preserved by a revision of #5 as: the fundamental characteristic of Socialism is the collectivization of Labor, from which the collectivization of Property can follow.