rw [← Ideal.comap_coe e, Ideal.comap_comap, ← e.toAlgHom_toRingHom, AlgHom.comp_algebraMap]
R : Type u_1
S₁ : Type u_2
S₂ : Type u_3
inst✝⁵ : CommRing R
inst✝⁴ : CommRing S₁
inst✝³ : CommRing S₂
inst✝² : Algebra R S₁
inst✝¹ : Algebra R S₂
e : S₁ ≃ₐ[R] S₂
p : Ideal R
P : Ideal S₂
inst✝ : p.IsMaximal
⊢ comap (algebraMap R S₁) (comap e P) = p ↔ comap (algebraMap R S₂) P = p
no goals