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	⊢ ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		pm2.21	⊢ ( ¬ 𝜑 → ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) )
2	1	a2i	⊢ ( ( ¬ 𝜑 → 𝜑 ) → ( ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) )
3	2	con4d	⊢ ( ( ¬ 𝜑 → 𝜑 ) → ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) )
4	3	pm2.43i	⊢ ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 )