Hoare triple for assignment P{x/E} x:=E {P}
Notice that what Wikipedia is saying is that


  The assignment axiom means that the truth of $\{P[x/E]\}$ is equivalent to the after-assignment truth of $\{P\}$.


In other words, ($P$ holds after the execution of $x:= E$) if ($P[x/E]$ holds before the execution). This is equivalent to the definition $A$ you provided, which is generally a more intuitive definition for Hoare triple.