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Theorem impexpdcom 37742
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 → ((𝜓𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
2:: ((𝜓 → (𝜒 → (𝜑𝜃))) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
qed:1,2: ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜓 → (𝜒 → (𝜑𝜃))))
Assertion
Ref Expression
impexpdcom ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜓 → (𝜒 → (𝜑𝜃))))

Proof of Theorem impexpdcom
StepHypRef Expression
1 impexpd 37740 . 2 ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
2 com3rgbi 37741 . 2 ((𝜓 → (𝜒 → (𝜑𝜃))) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
31, 2bitr4i 266 1 ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜓 → (𝜒 → (𝜑𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  wa 383
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 196  df-an 385
This theorem is referenced by: (None)
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