Mathbox for Alan Sare 
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Description: Join three logical equivalences to form equivalence of implications. imbi13 28283 is imbi13VD 28650 without virtual deductions and was automatically derived from imbi13VD 28650 using the tools program translate..without..overwriting.cmd and Metamath's minimize command. (Contributed by Alan Sare, 18Mar2012.) (Proof modification is discouraged.) (New usage is discouraged.) 
Ref  Expression 

imbi13 
Step  Hyp  Ref  Expression 

1  imbi12 28282  . 2  
2  imbi12 28282  . 2  
3  1, 2  syl9r 67  1 
Colors of variables: wff set class 
Syntax hints: wi 4 wb 176 
This theorem is referenced by: trsbc 28304 trsbcVD 28653 
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 