Theorem rp-7frege 44800

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 44790	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
2		rp-frege24 44796	. 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))))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44789  ax-frege2 44790

This theorem is used by:  axfrege8  44806