Theorem frege43 43830

Description: If there is a choice only between 𝜑 and 𝜑, then 𝜑 takes place. Identical to pm2.18 128. 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 43829	. 2 ⊢ ¬ ¬ (𝜑 → 𝜑)
2		frege40 43826	. 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 43773  ax-frege2 43774  ax-frege8 43792  ax-frege28 43813  ax-frege31 43817  ax-frege41 43828

This theorem is referenced by:  frege44  43831