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Theorem nfntht2 1720
Description: Closed form of nfnth 1728. (Contributed by BJ, 16-Sep-2021.)
Assertion
Ref Expression
nfntht2  |-  ( A. x  -.  ph  ->  F/ x ph )

Proof of Theorem nfntht2
StepHypRef Expression
1 olc 399 . 2  |-  ( A. x  -.  ph  ->  ( A. x ph  \/  A. x  -.  ph ) )
2 nf3 1712 . 2  |-  ( F/ x ph  <->  ( A. x ph  \/  A. x  -.  ph ) )
31, 2sylibr 224 1  |-  ( A. x  -.  ph  ->  F/ x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 383   A.wal 1481   F/wnf 1708
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710
This theorem is referenced by:  nfnth  1728
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