Mathbox for Alan Sare 
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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm2.43cbi  Unicode version 
Description: Logical equivalence of a 3leftnested implication and a 2leftnested
implicated when two antecedents of the former implication are identical.
(Contributed by Alan Sare, 18Mar2012.)
(Proof modification is discouraged.) (New usage is discouraged.)
The following User's Proof is
a Virtual Deduction proof completed automatically by the tools program
completeusersproof.cmd, which invokes Mel 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.

Ref  Expression 

pm2.43cbi 
Step  Hyp  Ref  Expression 

1  pm2.24 101  . . . 4  
2  1  com4l 78  . . 3 
3  id 19  . . 3  
4  2, 3  ja 153  . 2 
5  ax1 5  . 2  
6  4, 5  impbii 180  1 
Colors of variables: wff set class 
Syntax hints: wn 3 wi 4 wb 176 
This theorem is referenced by: ee233 28580 ee33VD 28971 
This theorem was proved from axioms: ax1 5 ax2 6 ax3 7 axmp 8 
This theorem depends on definitions: dfbi 177 
Copyright terms: Public domain  W3C validator 