Joseph-Pierre Proudhon believed in private property. This is demonstrably true. Under so-called usage based anarchism, the philosophy of most "anarcho"-collectivists, all ownership of property would be revoked upon transfer of usage. Therefore, all forms of usury, such as interest, rent, and wage labor would be criminal and abolished by force. However, in a debate with the classical liberal economist Frederic Bastiat, Proudhon stated that “Interest is neither a crime nor an offense”, and went on to say:
“this fundamental denial of Interest does not destroy, in our view, the principle – the right, if you will – which gives birth to Interest, and which has enabled it to continue to this day in spite of its condemnation by secular and ecclesiastical authority. So that the real problem before us is not to ascertain whether Usury, per se, is illegitimate (in this respect we are of the opinion of the Church), nor whether it has an excuse for its existence (on this point we agree with the economists). The problem is to devise a means of suppressing the abuse without violating the Right – a means, in a word, of reconciling this contradiction.”
From this, we can logically conclude that Proudhon did indeed subscribe to Locke’s perception of sticky property rights, same as Rothbard and other modern capitalist anarchists. Anarchism has historically believed in private property, and anarcho-capitalists are indeed anarchists.