Theorem: LO.FirstOrder.Structure.ElementaryEquiv.refl (Logic/FirstOrder/Basic/Semantics/Elementary.lean)

State before:
L : Language
M✝ : Type u_1
M₁ : Type u_2
M₂ : Type u_3
M₃ : Type u_4
inst✝⁵ : Nonempty M✝
inst✝⁴ : Nonempty M₁
inst✝³ : Nonempty M₂
inst✝² : Nonempty M₃
s : Structure L M✝
s₁ : Structure L M₁
s₂ : Structure L M₂
s₃ : Structure L M₃
M : Type u_5
inst✝¹ : Nonempty M
inst✝ : Structure L M
σ : Sentence L
⊢ M ⊧ₘ σ ↔ M ⊧ₘ σ
Tactic:
rfl
State after:
no goals