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Theorem nfrd 1454
Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfrd.1  |-  ( ph  ->  F/ x ps )
Assertion
Ref Expression
nfrd  |-  ( ph  ->  ( ps  ->  A. x ps ) )

Proof of Theorem nfrd
StepHypRef Expression
1 nfrd.1 . 2  |-  ( ph  ->  F/ x ps )
2 nfr 1452 . 2  |-  ( F/ x ps  ->  ( ps  ->  A. x ps )
)
31, 2syl 14 1  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   F/wnf 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  nfan1  1497  nfim1  1504  alrimdd  1541  spimed  1669  cbv2  1676  nfald  1684  sbied  1712  cbvexd  1844  sbcomxyyz  1888  hbsbd  1900  dvelimALT  1928  dvelimfv  1929  hbeud  1964  abidnf  2761  eusvnfb  4212
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