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Theorem nfr 1753
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 1535 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 sp 1728 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( ph  ->  A. x ph ) )
31, 2sylbi 187 1  |-  ( F/ x ph  ->  ( ph  ->  A. x ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   F/wnf 1534
This theorem is referenced by:  nfri  1754  nfrd  1755  nfald  1787  spimt  1927  sbft  1978  nfaldwAUX7  29429  spimtNEW7  29484  sbftNEW7  29531  ax7wnftAUX7  29627  nfaldOLD7  29644
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-nf 1535
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