Description: The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. The
completed Virtual Deduction Proof (not shown) was minimized. The
minimized proof is shown.
(Contributed by Alan Sare, 18Mar2012.)
(Proof modification is discouraged.) (New usage is discouraged.)
1::  ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃)))
→ (𝜑 → (𝜒 → (𝜓 → 𝜃))))
 2::  ⊢ ((𝜑 → (𝜒 → (𝜓 → 𝜃)))
→ (𝜒 → (𝜑 → (𝜓 → 𝜃))))
 3:1,2:  ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃)))
→ (𝜒 → (𝜑 → (𝜓 → 𝜃))))
 4::  ⊢ ((𝜒 → (𝜑 → (𝜓 → 𝜃)))
→ (𝜑 → (𝜒 → (𝜓 → 𝜃))))
 5::  ⊢ ((𝜑 → (𝜒 → (𝜓 → 𝜃)))
→ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
 6:4,5:  ⊢ ((𝜒 → (𝜑 → (𝜓 → 𝜃)))
→ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
 qed:3,6:  ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃)))
↔ (𝜒 → (𝜑 → (𝜓 → 𝜃))))

