Theorem frege38 40194

Description: Identical to pm2.21 123. Proposition 38 of [Frege1879] p. 46. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem frege38

Step	Hyp	Ref	Expression
1		frege36 40192	. 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜓))
2		ax-frege8 40162	. 2 ⊢ ((𝜑 → (¬ 𝜑 → 𝜓)) → (¬ 𝜑 → (𝜑 → 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 40143  ax-frege2 40144  ax-frege8 40162  ax-frege28 40183  ax-frege31 40187

This theorem is referenced by:  frege39  40195