How does Upsilon know which values from other basic blocks it could receive? That information is critical for transformations like constant propagation, and register allocation.
Upsilon uses an SSA value, and assigns to a Phi. The use of an SSA value is just a normal SSA use.
The assignment to the Phi is special, and follows Static Single Use law.
In practice, you'll want to either have all Phis know about the Upsilons that refer to them, or you'll want to have a handy analysis that tells you about the Upsilons that refer to Phis. This part is no different from how your SSA form will either have user tracking (like LLVM IR) or an analysis that tells you the users.