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Description: A proposition is equivalent to it being implied by . Closed form of trud 1446 (which it can shorten); dual of dfnot 1456. It is to tbtru 1447 what a1bi 338 is to tbt 345, and this appears in their respective proofs. (Contributed by BJ, 26Oct2019.) (Proof modification is discouraged.) 
Ref  Expression 

bjtrut 
Step  Hyp  Ref  Expression 

1  tru 1441  . 2  
2  1  a1bi 338  1 
Colors of variables: wff setvar class 
Syntax hints: wi 4 wb 187 wtru 1438 
This theorem was proved from axioms: axmp 5 ax1 6 ax2 7 ax3 8 
This theorem depends on definitions: dfbi 188 dftru 1440 
This theorem is referenced by: (None) 
Copyright terms: Public domain  W3C validator 