NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  hbth Unicode version

Theorem hbth 1552
Description: No variable is (effectively) free in a theorem.

This and later "hypothesis-building" 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, 5-Aug-1993.)

Ref Expression
Ref Expression

Proof of Theorem hbth
StepHypRef Expression
1 hbth.1 . . 3
21ax-gen 1546 . 2
32a1i 10 1
Colors of variables: wff setvar class
Syntax hints:   wi 4  wal 1540
This theorem was proved from axioms:  ax-1 5  ax-mp 8  ax-gen 1546
This theorem is referenced by:  nfth  1553  spfalw  1672  spimehOLD  1821
  Copyright terms: Public domain W3C validator