Theorem luklem5

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	luklem5	$$⊢\phi \to \left(\psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		luklem3	$$⊢\phi \to \left(\left(\left(\neg \phi \to \phi \right)\to \phi \right)\to \left(\psi \to \phi \right)\right)$$
2		luklem4	$$⊢\left(\left(\left(\neg \phi \to \phi \right)\to \phi \right)\to \left(\psi \to \phi \right)\right)\to \left(\psi \to \phi \right)$$
3	1 2	luklem1	$$⊢\phi \to \left(\psi \to \phi \right)$$