Theorem frege43

Description: If there is a choice only between ph and ph , then ph takes place. Identical to pm2.18 . Proposition 43 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege43	⊢ ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		frege42	⊢ ¬ ¬ ( 𝜑 → 𝜑 )
2		frege40	⊢ ( ¬ ¬ ( 𝜑 → 𝜑 ) → ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) )
3	1 2	ax-mp	⊢ ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 )