Equality saturation is a semantics-based technique for automatically and efficiently proving that two programs are equivalent modulo a fixed set of equality axioms. In this paper, we extend the equality saturation technique with contextual reasoning in order to perform rewriting under assumptions that are locally valid inside a conditional branch. This is based on a new notion of cyclic e-graphs with contextual annotations. We experimentally validate the efficiency and scalability of this new technique by proving equivalence of several families of programs where contextual reasoning is required.