Theorem rp-7frege 40154

Description: Distribute antecedent and add another. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
rp-7frege	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜃 → ((𝜑 → 𝜓) → (𝜑 → 𝜒))))

Proof of Theorem rp-7frege

Step	Hyp	Ref	Expression
1		ax-frege2 40144	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
2		rp-frege24 40150	. 2 ⊢ (((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒))) → ((𝜑 → (𝜓 → 𝜒)) → (𝜃 → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜃 → ((𝜑 → 𝜓) → (𝜑 → 𝜒))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 40143  ax-frege2 40144

This theorem is referenced by:  axfrege8  40160