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Theorem nfd 1933
Description: Deduce that  x is not free in  ps 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 1932 . 2  |-  ( ph  ->  A. x ( ps 
->  A. x ps )
)
4 df-nf 1662 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
53, 4sylibr 215 1  |-  ( ph  ->  F/ x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   F/wnf 1661
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662
This theorem is referenced by:  nfdh  1934  nfnt  1959  axc16nf  2004  nfald  2011  dvelimhw  2015  cbv1h  2076  nfeqf  2104  axc16nfALT  2124  nfsb2  2157  distel  30457  bj-cbv1hv  31293  bj-axc16nf  31323  bj-nfsb2v  31339  wl-ax11-lem3  31881
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