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Theorem impexpd 39244
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 437 . 2 (((𝜓𝜒) → 𝜃) ↔ (𝜓 → (𝜒𝜃)))
21imbi2i 325 1 ((𝜑 → ((𝜓𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 382
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 197  df-an 383
This theorem is referenced by:  impexpdcom  39246
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