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Theorem nfr 1456
Description: Consequence of the definition of not-free. (Contributed by Mario Carneiro, 26-Sep-2016.)
Assertion
Ref Expression
nfr  |-  ( F/ x ph  ->  ( ph  ->  A. x ph )
)

Proof of Theorem nfr
StepHypRef Expression
1 df-nf 1395 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 sp 1446 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( ph  ->  A. x ph ) )
31, 2sylbi 119 1  |-  ( F/ x ph  ->  ( ph  ->  A. x ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287   F/wnf 1394
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1445
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  nfri  1457  nfrd  1458  nfimd  1522  19.23t  1612  equs5or  1758  sbequi  1767  sbft  1776  sbcomxyyz  1894  rgen2a  2429
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