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Theorem impexpdcom 42135
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 42133 . 2 ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
2 com3rgbi 42134 . 2 ((𝜓 → (𝜒 → (𝜑𝜃))) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
31, 2bitr4i 277 1 ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜓 → (𝜒 → (𝜑𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 396
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 206  df-an 397
This theorem is referenced by: (None)
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