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Theorem nfd 1746
Description: Deduce that  x is not free in  ph in a context. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
nfd.1  |-  F/ x ph
nfd.2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Assertion
Ref Expression
nfd  |-  ( ph  ->  F/ x ps )

Proof of Theorem nfd
StepHypRef Expression
1 nfd.1 . . 3  |-  F/ x ph
2 nfd.2 . . 3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
31, 2alrimi 1745 . 2  |-  ( ph  ->  A. x ( ps 
->  A. x ps )
)
4 df-nf 1532 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
53, 4sylibr 203 1  |-  ( ph  ->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   F/wnf 1531
This theorem is referenced by:  nfdh  1747  nfnd  1760  nfald  1775  nfeqf  1898  dvelimf  1937  a16nf  1991  nfsb2  1998  sbal2  2073  copsexg  4252  riotasv2dOLD  6350  riotasv3dOLD  6354  distel  24160
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-nf 1532
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