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Mirrors > Home > MPE Home > Th. List > hbth  Structured version 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, 11May1993.) 
Ref  Expression 

hbth.1 
Ref  Expression 

hbth 
Step  Hyp  Ref  Expression 

1  hbth.1  . . 3  
2  1  axgen 1639  . 2 
3  2  a1i 11  1 
Colors of variables: wff setvar class 
Syntax hints: wi 4 wal 1403 
This theorem was proved from axioms: axmp 5 ax1 6 axgen 1639 
This theorem is referenced by: nfth 1646 spfalw 1810 
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