Theorem frege39 44842

Description: Syllogism between pm2.18 129 and pm2.24 125. 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 44841	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2		ax-frege2 44791	. 2 ⊢ ((¬ 𝜑 → (𝜑 → 𝜓)) → ((¬ 𝜑 → 𝜑) → (¬ 𝜑 → 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ ((¬ 𝜑 → 𝜑) → (¬ 𝜑 → 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44790  ax-frege2 44791  ax-frege8 44809  ax-frege28 44830  ax-frege31 44834

This theorem is used by:  frege40  44843