Generally Rolle's theorem is expressed with words. But how should it look in a formal mathematical/logic language?
$$\forall f \Big( \big(f \textrm{continue [a,b]} \land f \textrm{differentiable ]a,b[} \land f(a)=f(b) \big) \rightarrow \exists c \in ]a,b[\textrm{ s.t. }f'(c)=0 \Big)$$
$$\forall f \Big( (f \textrm{continue [a,b]} \land f \textrm{differentiable ]a,b[ }) ( f(a)=f(b) \rightarrow \exists c \in ]a,b[\textrm{ s.t. }f'(c)=0) \Big)$$
So where should we place $f(a)=f(b)$ ?
The two formulations are logically equivalent. Indeed, $(A \land B) \to C$ is logically equivalent to $A \to (B \to C)$ (you can check it by yourself by truth table). This equivalence is called currying in several contexts of mathematics and theoretical computer science.
Note that, to be more precise, the correct formalization of the second sentence is \begin{equation} \forall f \, \big( (f \text{ cont. }[a,b] \land f \text{ diff. } ]a,b[) \to (f(a) = f(b) \to \exists c (c \in {]a,b[} \land f'(c) = 0)) \big) \end{equation} (notice the nested implications).