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Theorem impexpd 40724
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:: (((𝜓𝜒) → 𝜃) ↔ (𝜓 → (𝜒 𝜃)))
qed:1: ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
Assertion
Ref Expression
impexpd ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))

Proof of Theorem impexpd
StepHypRef Expression
1 impexp 451 . 2 (((𝜓𝜒) → 𝜃) ↔ (𝜓 → (𝜒𝜃)))
21imbi2i 337 1 ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  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 208  df-an 397
This theorem is referenced by:  impexpdcom  40726
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