Theorem frege38

Description: Identical to pm2.21 . Proposition 38 of Frege1879 p. 46. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege38	⊢ ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		frege36	⊢ ( 𝜑 → ( ¬ 𝜑 → 𝜓 ) )
2		ax-frege8	⊢ ( ( 𝜑 → ( ¬ 𝜑 → 𝜓 ) ) → ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) )