Theorems · Theorem · ring theory

AlgHom.congr_fun

∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] {φ₁ φ₂ : A →ₐ[R] B}, φ₁ = φ₂ → ∀ (x : A), φ₁ x = φ₂ x

Defined in

Mathlib.Algebra.Algebra.Hom

Cited by

40 results in Mathlib

Foundations

Depth 21 from the axioms · uses no axioms

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra