The TLA + Proof System (TLAPS) allows users to verify proofs with the support of automated theorem provers, including SMT solvers. To increase trust in TLAPS, we revisited the encoding of TLA + for SMT, whose implementation had become too complex. Our approach is based on a first-order axiomatization with E-matching patterns. The new encoding is available with TLAPS and achieves performances similar to the previous version, despite its simpler design.