Packet transformers are widely used in ISPs, datacenter infrastructures, and layer-2 networks. Existing network verification tools do not scale to large networks with transformers (e.g., MPLS, IP-in-IP, and NAT). Toward scalable verification, we conceived a novel packet equivalence relation. For networks with packet transformers, we first present a formal definition of the packet equivalence relation. Our transformer model is general, including most transformers used in real networks. We also present a new definition of atomic predicates that specify the coarsest equivalence classes of packets in the packet space. We designed an algorithm for computing these atomic predicates. We built a verifier, named Atomic Predicates for Transformers, and evaluated its performance using four network data sets with MPLS tunnels, IP-in-IP tunnels, and NATs. For a provider cone data set with 11.6 million forwarding rules, 92 routers, 1920 duplex ports, and 40 MPLS tunnels which use 170 transformers, APT used only 0.065 s, on average, to compute the reachability tree from a source port to all other ports for all packets and perform loop detection as well. For the Stanford and Internet2 data sets with NATs, APT is faster than HSA (Hassel in C implementation) by two to three orders of magnitude. By working with atomic predicates instead of individual packets, APT achieves verification performance gains by orders of magnitude.