Mathbox for Alan Sare 
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee1111  Unicode version 
Description: Nonvirtual deduction form of e1111 28752. (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 

ee1111.1  
ee1111.2  
ee1111.3  
ee1111.4  
ee1111.5 
Ref  Expression 

ee1111 
Step  Hyp  Ref  Expression 

1  ee1111.4  . 2  
2  ee1111.1  . . 3  
3  ee1111.2  . . 3  
4  ee1111.3  . . 3  
5  ee1111.5  . . 3  
6  2, 3, 4, 5  syl3c 57  . 2 
7  1, 6  mpd 14  1 
Colors of variables: wff set class 
Syntax hints: wi 4 
This theorem is referenced by: e1111 28752 
This theorem was proved from axioms: ax1 5 ax2 6 axmp 8 
Copyright terms: Public domain  W3C validator 