Theorem impexpd 40867

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. After the User's Proof was completed, it was minimized. The completed User's Proof before minimization is not shown. (Contributed by Alan Sare, 18-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

1::	⊢ (((𝜓 ∧ 𝜒) → 𝜃) ↔ (𝜓 → (𝜒 → 𝜃)))
qed:1:	⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))

Assertion

Ref	Expression
impexpd	⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))

Proof of Theorem impexpd

Step	Hyp	Ref	Expression
1		impexp 453	. 2 ⊢ (((𝜓 ∧ 𝜒) → 𝜃) ↔ (𝜓 → (𝜒 → 𝜃)))
2	1	imbi2i 338	1 ⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))

Syntax hints:   → wi 4   ↔ wb 208   ∧ wa 398

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-an 399

This theorem is referenced by:  impexpdcom  40869