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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(** This module states propositional extensionality and draws
    consequences of it *)

Axiom propositional_extensionality :
  forall (P Q : Prop), (P <-> Q) -> P = Q.

Require Import ClassicalFacts.

Theorem proof_irrelevance : forall (P:Prop) (p1 p2:P), p1 = p2.
Proof.
  apply ext_prop_dep_proof_irrel_cic.
  exact propositional_extensionality.
Qed.