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Theorem nfr 1923
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 1664 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 sp 1909 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( ph  ->  A. x ph ) )
31, 2sylbi 198 1  |-  ( F/ x ph  ->  ( ph  ->  A. x ph )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   F/wnf 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-12 1904
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-nf 1664
This theorem is referenced by:  nfri  1924  nfrd  1925  19.21t  1958  19.23tOLD  1964  nfimd  1972  sbft  2171  bj-alrim  31227  bj-nexdt  31231  bj-cbv3tb  31252  bj-nfs1t2  31256  bj-sbftv  31326  bj-equsal1t  31376  stdpc5t  31381  wl-nfeqfb  31778
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