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Theorem nfr 1427
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 1366 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 sp 1417 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( ph  ->  A. x ph ) )
31, 2sylbi 118 1  |-  ( F/ x ph  ->  ( ph  ->  A. x ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1257   F/wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-4 1416
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  nfri  1428  nfrd  1429  nfimd  1493  19.23t  1583  equs5or  1727  sbequi  1736  sbft  1744  sbcomxyyz  1862  rgen2a  2392
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