Theorem impexpdcom 45257

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, 18-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

1::	⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
2::	⊢ ((𝜓 → (𝜒 → (𝜑 → 𝜃))) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
qed:1,2:	⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜓 → (𝜒 → (𝜑 → 𝜃))))

Assertion

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

Proof of Theorem impexpdcom

Step	Hyp	Ref	Expression
1		impexpd 45255	. 2 ⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
2		com3rgbi 45256	. 2 ⊢ ((𝜓 → (𝜒 → (𝜑 → 𝜃))) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃))))
3	1, 2	bitr4i 281	1 ⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜓 → (𝜒 → (𝜑 → 𝜃))))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by: (None)