Theorem frege39 40179

Description: Syllogism between pm2.18 128 and pm2.24 124. Proposition 39 of [Frege1879] p. 46. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege39	⊢ ((¬ 𝜑 → 𝜑) → (¬ 𝜑 → 𝜓))

Proof of Theorem frege39

Step	Hyp	Ref	Expression
1		frege38 40178	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2		ax-frege2 40128	. 2 ⊢ ((¬ 𝜑 → (𝜑 → 𝜓)) → ((¬ 𝜑 → 𝜑) → (¬ 𝜑 → 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ ((¬ 𝜑 → 𝜑) → (¬ 𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 40127  ax-frege2 40128  ax-frege8 40146  ax-frege28 40167  ax-frege31 40171

This theorem is referenced by:  frege40  40180