Strong completeness for the predicate logic of the continuous t-norms

The axiomatic system introduced by H\'ajek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom (∀ x φ)² ↔ ∀ x φ² and the infinitary rule \[ φ (α → β^n):n ∈ N/φ (α → α & β) \] to achieve strong completeness with respect to continuous t-norms.