Description: Logical equivalence of a 2leftnested implication and a 1leftnested
implicated
when two antecedents of the former implication are identical.
(Contributed by Alan Sare, 18Mar2012.)
(Proof modification is discouraged.) (New usage is discouraged.)
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.
1::  ⊢ ((𝜑 → (𝜓 → (𝜑 → 𝜒)))
→ (𝜑 → (𝜑 → (𝜓 → 𝜒))))
 2::  ⊢ ((𝜑 → (𝜑 → (𝜓 → 𝜒)))
→ (𝜑 → (𝜓 → 𝜒)))
 3:1,2:  ⊢ ((𝜑 → (𝜓 → (𝜑 → 𝜒)))
→ (𝜑 → (𝜓 → 𝜒)))
 4::  ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓
→ (𝜑 → 𝜒)))
 5:3,4:  ⊢ ((𝜑 → (𝜓 → (𝜑 → 𝜒)))
→ (𝜓 → (𝜑 → 𝜒)))
 6::  ⊢ ((𝜓 → (𝜑 → 𝜒)) → (𝜑
→ (𝜓 → (𝜑 → 𝜒))))
 qed:5,6:  ⊢ ((𝜑 → (𝜓 → (𝜑 → 𝜒)))
↔ (𝜓 → (𝜑 → 𝜒)))

