Fixpoint equations introduce variables via recursive definitions, enabling reasoning about infinitely defined structures such as streams. We combine efficient reasoning over equalities with reasoning over infinite structures within an e-graph to prove the equality of recursively defined variables. We extend the typical e-graph semantics to represent recursively defined variables and give an e-graph specific definition of bisimilarity. The key idea is to add secondary definitional edges to the e-graph that link, but do not merge, a variable with its definition. We identify three main challenges and sketch solutions to each of them.