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	$$⊢\left(\phi \vee \left(\phi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \phi \to \left(\phi \to \psi \right)$$
2	1	orri	$$⊢\left(\phi \vee \left(\phi \to \psi \right)\right)$$