MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nffal Structured version   Visualization version   GIF version

Theorem nffal 1772
Description: The false constant has no free variables (see nftru 1770). (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
nffal 𝑥

Proof of Theorem nffal
StepHypRef Expression
1 fal 1530 . 2 ¬ ⊥
21nfnth 1768 1 𝑥
Colors of variables: wff setvar class
Syntax hints:  wfal 1528  wnf 1748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762
This theorem depends on definitions:  df-bi 197  df-or 384  df-tru 1526  df-fal 1529  df-ex 1745  df-nf 1750
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator