1) With respect to any occurrent (as opposed to dispositional) belief, there is a distinction between the mental act of believing and the content believed. Since believing is 'intentional' as philosophers use this term, i.e., necessarily object-directed, there cannot be an act of believing that is not directed upon some object or content. To believe is to believe something, that the door has been left ajar, for example. Nevertheless, the believing and the believed are distinct.
2) The contents of believings have properties that belief-states lack. For one thing, belief-contents are shareable. That the door has been left ajar, that Frege died in 1925, that both 2 and -2 are roots of 4, are contents to which more than one mind has access. But the psychological state that I am in when I believe that the door is ajar is not shareable in the same sense. Second, the belief-contents can be accepted, rejected, entertained, etc., which is not the case for the corresponding believings, disbelievings, and entertainings unless of course these believings, etc. become the objects of higher order beliefs. Third, belief contents are either true or false, which cannot be said in exactly same sense of believings, etc.
3) There are occurrent beliefs.
Therefore
4) There are propositions.
The argument is to the conclusion that something or other must play the roles of truth-bearer, object of such attitudes as knowing and believing, and ground of the possibility of two or more minds' coming to believe or know the same thing. It is an argument for the existence of propositions that leaves open their exact nature.