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Metamath Proof Explorer

Theorem curryax

Description: A non-intuitionistic positive statement, sometimes called a paradox of material implication. Sometimes called Curry's axiom. Similar to exmid (obtained by substituting F. for ps ) but positive. For another non-intuitionistic positive statement, see peirce . (Contributed by BJ, 4-Apr-2021)

		Ref	Expression
	Assertion	curryax	$⊢ (φ \lor (φ \to ψ))$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$⊢ \neg φ \to (φ \to ψ)$
2	1	orri	$⊢ (φ \lor (φ \to ψ))$