Theorem frege6 41414

Description: A closed form of imim2d 57 which is a deduction adding nested antecedents. Proposition 6 of [Frege1879] p. 33. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege6	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → ((𝜃 → 𝜓) → (𝜃 → 𝜒))))

Proof of Theorem frege6

Step	Hyp	Ref	Expression
1		frege5 41408	. 2 ⊢ ((𝜓 → 𝜒) → ((𝜃 → 𝜓) → (𝜃 → 𝜒)))
2		frege5 41408	. 2 ⊢ (((𝜓 → 𝜒) → ((𝜃 → 𝜓) → (𝜃 → 𝜒))) → ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → ((𝜃 → 𝜓) → (𝜃 → 𝜒)))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → ((𝜃 → 𝜓) → (𝜃 → 𝜒))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 41398  ax-frege2 41399

This theorem is referenced by:  frege7  41416