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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 ∨ ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.21	⊢ ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) )
2	1	orri	⊢ ( 𝜑 ∨ ( 𝜑 → 𝜓 ) )