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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(** 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.
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