Theorem pm2.18OLD

Description: Obsolete version of pm2.18 as of 17-Nov-2023. (Contributed by NM, 29-Dec-1992) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	pm2.18OLD	$$⊢\left(\neg \phi \to \phi \right)\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \phi \to \left(\phi \to \neg \left(\neg \phi \to \phi \right)\right)$$
2	1	a2i	$$⊢\left(\neg \phi \to \phi \right)\to \left(\neg \phi \to \neg \left(\neg \phi \to \phi \right)\right)$$
3	2	con4d	$$⊢\left(\neg \phi \to \phi \right)\to \left(\left(\neg \phi \to \phi \right)\to \phi \right)$$
4	3	pm2.43i	$$⊢\left(\neg \phi \to \phi \right)\to \phi$$