By basing Bayesian probability theory on flve axioms, we can give a trivial proof of Cox's Theorem on the product rule and sum rule for conditional plausibility without assuming continuity or difierentiablity of plausibility. Instead, we extend the notion of plausibility to apply to unknowns, giving them plausi- ble values. Thus, we combine the best aspects of two approaches to Bayesian probability theory, namely the Cox-Jaynes theory and the de Finetti theory. The problem of developing the foundations of Laplacian or Bayesian probability has led to many difierent approaches, which are mainly variations on two. The flrst, which is our main concern is due to R. T. Cox (1961). The second is due to Bruno de Finetti (1974), de Finetti (1975) and a concise general treatment is in Regazzini (1985). We flnd that by combining aspects of both, we can substantially weaken the assumptions and arrive at a proof of the problematic Cox theorem which is very simple, in fact trivial, as it should be. This triviality is of the utmost importance. The foundational axioms assumed by de Finetti for conditional expectation (his conditional prevision) require a positive normalized linear functional on a partially ordered commutative algebra (with identity element and over the reals) of objects more general than random variables which he calls \random quantities and which we will simply call \unknowns or \unknown numerical quantities. Even though it is not explicitly pointed out axiomatically, de Finetti, in his discussion in the flrst two chapters of his book, assumes that the ordering of the lattice of idempotents is inherited from that of the algebra. To deflne his conditional prevision, he requires a coherence condition (see also Regazzini (1985)) equivalent to a quadratic minimization property assumed to be satisfled by the choice of previsions. We merely assume the existence of some form of rules and demonstrate that if the assignment of plausible value (what de Finetti calls \prevision) is required to be logically consistent, then the actual rules themselves are uniquely determined. In particular, as a conse- quence, the rules of conditional expectation in Bayesian probability theory are uniquely determined by the requirement of logical consistency. Thus we flnd a trivial proof of the Cox Theorem, which properly understood, is a uniqueness theorem, and we show that the theory of de Finetti is a consequence. That is, de Finetti assumes his coherence condition, meaning existence of a positive linear functional which also satisfles a cer- tain quadratic minimization criteria, and he uses the quadratic minimization criteria to