chore: Remove Init.Propext (#10709)

These lemmas can easily go to `Logic.Basic`

Author: YaelDillies

Mathlib.lean

@@ -2485,7 +2485,6 @@ import Mathlib.Init.Logic
 import Mathlib.Init.Meta.WellFoundedTactics
 import Mathlib.Init.Order.Defs
 import Mathlib.Init.Order.LinearOrder
-import Mathlib.Init.Propext
 import Mathlib.Init.Quot
 import Mathlib.Init.Set
 import Mathlib.Init.ZeroOne

Mathlib/CategoryTheory/IsConnected.lean

@@ -185,7 +185,7 @@ The converse is given in `IsConnected.of_induct`.
 -/
 theorem induct_on_objects [IsPreconnected J] (p : Set J) {j₀ : J} (h0 : j₀ ∈ p)
     (h1 : ∀ {j₁ j₂ : J} (_ : j₁ ⟶ j₂), j₁ ∈ p ↔ j₂ ∈ p) (j : J) : j ∈ p := by
-  let aux (j₁ j₂ : J) (f : j₁ ⟶ j₂) := congrArg ULift.up <| (h1 f).to_eq
+  let aux (j₁ j₂ : J) (f : j₁ ⟶ j₂) := congrArg ULift.up <| (h1 f).eq
   injection constant_of_preserves_morphisms (fun k => ULift.up.{u₁} (k ∈ p)) aux j j₀ with i
   rwa [i]
 #align category_theory.induct_on_objects CategoryTheory.induct_on_objects

Mathlib/GroupTheory/GroupAction/Quotient.lean

@@ -427,7 +427,7 @@ theorem card_comm_eq_card_conjClasses_mul_card (G : Type*) [Group G] :
   rw [card_congr (Equiv.subtypeProdEquivSigmaSubtype Commute), card_sigma,
     sum_equiv ConjAct.toConjAct.toEquiv (fun a ↦ card { b // Commute a b })
       (fun g ↦ card (MulAction.fixedBy G g))
-      fun g ↦ card_congr' <| congr_arg _ <| funext fun h ↦ mul_inv_eq_iff_eq_mul.symm.to_eq,
+      fun g ↦ card_congr' <| congr_arg _ <| funext fun h ↦ mul_inv_eq_iff_eq_mul.symm.eq,
     MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group]
   congr 1; apply card_congr'; congr; ext;
   exact (Setoid.comm' _).trans isConj_iff.symm

Mathlib/Init/Propext.lean

@@ -923,6 +923,26 @@ theorem forall_prop_congr' {p p' : Prop} {q q' : p → Prop} (hq : ∀ h, q h 
   propext (forall_prop_congr hq hp)
 #align forall_prop_congr' forall_prop_congr'
 
+#align forall_congr_eq forall_congr
+
+lemma imp_congr_eq {a b c d : Prop} (h₁ : a = c) (h₂ : b = d) : (a → b) = (c → d) :=
+  propext (imp_congr h₁.to_iff h₂.to_iff)
+
+lemma imp_congr_ctx_eq {a b c d : Prop} (h₁ : a = c) (h₂ : c → b = d) : (a → b) = (c → d) :=
+  propext (imp_congr_ctx h₁.to_iff fun hc ↦ (h₂ hc).to_iff)
+
+lemma eq_true_intro (h : a) : a = True := propext (iff_true_intro h)
+lemma eq_false_intro (h : ¬a) : a = False := propext (iff_false_intro h)
+
+-- FIXME: `alias` creates `def Iff.eq := propext` instead of `lemma Iff.eq := propext`
+@[nolint defLemma] alias Iff.eq := propext
+
+lemma iff_eq_eq : (a ↔ b) = (a = b) := propext ⟨propext, Eq.to_iff⟩
+
+-- They were not used in Lean 3 and there are already lemmas with those names in Lean 4
+#noalign eq_false
+#noalign eq_true
+
 /-- See `IsEmpty.forall_iff` for the `False` version. -/
 @[simp] theorem forall_true_left (p : True → Prop) : (∀ x, p x) ↔ p True.intro :=
   forall_prop_of_true _

Mathlib/Logic/Basic.lean

@@ -5,7 +5,6 @@ Authors: Johannes Hölzl
 -/
 import Mathlib.Logic.Function.Basic
 import Mathlib.Logic.Relator
-import Mathlib.Init.Propext
 import Mathlib.Init.Data.Quot
 import Mathlib.Tactic.Cases
 import Mathlib.Tactic.Use

Mathlib/Logic/Relation.lean

@@ -1477,7 +1477,7 @@ theorem EventuallyEq.rw {l : Filter α} {f g : α → β} (h : f =ᶠ[l] g) (p :
 #align filter.eventually_eq.rw Filter.EventuallyEq.rw
 
 theorem eventuallyEq_set {s t : Set α} {l : Filter α} : s =ᶠ[l] t ↔ ∀ᶠ x in l, x ∈ s ↔ x ∈ t :=
-  eventually_congr <| eventually_of_forall fun _ => ⟨Eq.to_iff, Iff.to_eq⟩
+  eventually_congr <| eventually_of_forall fun _ ↦ eq_iff_iff
 #align filter.eventually_eq_set Filter.eventuallyEq_set
 
 alias ⟨EventuallyEq.mem_iff, Eventually.set_eq⟩ := eventuallyEq_set