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Theorem impexpdcom 41693
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 41691 . 2 ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
2 com3rgbi 41692 . 2 ((𝜓 → (𝜒 → (𝜑𝜃))) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
31, 2bitr4i 281 1 ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜓 → (𝜒 → (𝜑𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator