Then what does imply turing completeness?
According to the wikipedia article [1]:
"To show that something is Turing complete, it is enough to show that it can be used to simulate some Turing complete system. For example, an imperative language is Turing complete if it has conditional branching (e.g., "if" and "goto" statements, or a "branch if zero" instruction; see one instruction set computer) and the ability to change an arbitrary amount of memory (e.g., the ability to maintain an arbitrary number of variables). Since this is almost always the case, most if not all imperative languages are Turing complete if the limitations of finite memory are ignored."