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Theorem nfr 1483
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 1422 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 sp 1473 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( ph  ->  A. x ph ) )
31, 2sylbi 120 1  |-  ( F/ x ph  ->  ( ph  ->  A. x ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314   F/wnf 1421
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1472
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  nfri  1484  nfrd  1485  nfimd  1549  19.23t  1640  equs5or  1786  sbequi  1795  sbft  1804  sbcomxyyz  1923  rgen2a  2463
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