Theorem pm2.83 85

Description: Theorem *2.83 of [WhiteheadRussell] p. 108. Closed form of syld 48. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.83	⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → (𝜒 → 𝜃)) → (𝜑 → (𝜓 → 𝜃))))

Proof of Theorem pm2.83

Step	Hyp	Ref	Expression
1		imim1 84	. 2 ⊢ ((𝜓 → 𝜒) → ((𝜒 → 𝜃) → (𝜓 → 𝜃)))
2	1	imim3i 65	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → (𝜒 → 𝜃)) → (𝜑 → (𝜓 → 𝜃))))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by: (None)