Mathbox for Alan Sare 
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Mirrors > Home > MPE Home > Th. List > Mathboxes > impexpd  Structured version Visualization version GIF version 
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,
18Mar2012.) (Proof modification is discouraged.)
(New usage is discouraged.)

Ref  Expression 

impexpd  ⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃)))) 
Step  Hyp  Ref  Expression 

1  impexp 454  . 2 ⊢ (((𝜓 ∧ 𝜒) → 𝜃) ↔ (𝜓 → (𝜒 → 𝜃)))  
2  1  imbi2i 339  1 ⊢ ((𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃)))) 
Colors of variables: wff setvar class 
Syntax hints: → wi 4 ↔ wb 209 ∧ wa 399 
This theorem was proved from axioms: axmp 5 ax1 6 ax2 7 ax3 8 
This theorem depends on definitions: dfbi 210 dfan 400 
This theorem is referenced by: impexpdcom 41639 
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