The TLA+ Proof System (TLAPS) allows users to verify proofs with the support of automated provers, including SMT solvers. To better ensure the soundness of TLAPS, we revisited the encoding of TLA+ into SMT-LIB, 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.