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Mirrors > Home > MPE Home > Th. List > hbth  Unicode version 
Description: No variable is
(effectively) free in a theorem.
This and later "hypothesisbuilding" lemmas, with labels starting "hb...", allow us to construct proofs of formulas of the form from smaller formulas of this form. These are useful for constructing hypotheses that state " is (effectively) not free in ." (Contributed by NM, 5Aug1993.) 
Ref  Expression 

hbth.1 
Ref  Expression 

hbth 
Step  Hyp  Ref  Expression 

1  hbth.1  . . 3  
2  1  axgen 1533  . 2 
3  2  a1i 10  1 
Colors of variables: wff set class 
Syntax hints: wi 4 wal 1527 
This theorem is referenced by: nfth 1540 spimeh 1722 ax9lem12 29151 ax9lem13 29152 
This theorem was proved from axioms: ax1 5 axmp 8 axgen 1533 
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