have claim1 := repl_in_model_sat_iff x ψ φ1 M w
φ1 φ2 : Formula
x : ℕ
ψ : Formula
hyp : φ1≡φ2
W : Type
M : KripkeModel W
w : W
⊢ evaluate M w (repl_in_F x ψ φ1) ↔ evaluate M w (repl_in_F x ψ φ2)
φ1 φ2 : Formula
x : ℕ
ψ : Formula
hyp : φ1≡φ2
W : Type
M : KripkeModel W
w : W
claim1 : (M, w)⊨repl_in_F x ψ φ1 ↔ (repl_in_model x ψ M, w)⊨φ1
⊢ evaluate M w (repl_in_F x ψ φ1) ↔ evaluate M w (repl_in_F x ψ φ2)