MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfth Unicode version

Theorem nfth 1540
Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
hbth.1  |-  ph
Assertion
Ref Expression
nfth  |-  F/ x ph

Proof of Theorem nfth
StepHypRef Expression
1 hbth.1 . . 3  |-  ph
21hbth 1539 . 2  |-  ( ph  ->  A. x ph )
32nfi 1538 1  |-  F/ x ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1531
This theorem is referenced by:  nftru  1541  nfequid  1645  sbt  1973  sbc2ie  3058  uzindOLD  10106  infcvgaux1i  12315  exnel  24159  a12lem1  29130
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533
This theorem depends on definitions:  df-bi 177  df-nf 1532
  Copyright terms: Public domain W3C validator