According to the article on Hilbert's Axioms for Euclidean Geometry on Wikipedia, axioms I.4 and I.5 are as follows:
For every three points $A, B, C$ not situated on the same line there exists a plane $α$ that contains all of them. For every plane there exists a point which lies on it. We write $ABC = α$. We employ also the expressions: "$A, B, C$ lie in $α$"; "$A, B, C$ are points of $α$", etc.
For every three points $A, B, C$ which do not lie in the same line, there exists no more than one plane that contains them all.
What struck me as odd was how the first part of axiom I.4 and the entirety of I.5 were laid out. What is the reasoning behind breaking up these two axioms in this way? If axiom I.4 had been rewritten as
For every three points $A, B, C$ not situated on the same line there exists exactly one plane $α$ that contains all of them. For every plane there exists a point which lies on it. We write $ABC = α$. We employ also the expressions: "$A, B, C$ lie in $α$"; "$A, B, C$ are points of $α$", etc.
wouldn't it automatically encapsulate the other two? Aren't the first two equivalent to the one proposed? Is there a reason this one axiom was broken up into two separate ones, even if just aesthetic?