Theorem frege43 38141

Description: If there is a choice only between 𝜑 and 𝜑, then 𝜑 takes place. Identical to pm2.18 122. Proposition 43 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem frege43

Step	Hyp	Ref	Expression
1		frege42 38140	. 2 ⊢ ¬ ¬ (𝜑 → 𝜑)
2		frege40 38137	. 2 ⊢ (¬ ¬ (𝜑 → 𝜑) → ((¬ 𝜑 → 𝜑) → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ((¬ 𝜑 → 𝜑) → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103  ax-frege28 38124  ax-frege31 38128  ax-frege41 38139

This theorem is referenced by:  frege44  38142