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Theorem nfntOLDOLD 1783
Description: Obsolete proof of nfnt 1782 as of 3-Nov-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 28-Dec-2017.) (Revised by BJ, 24-Jul-2019.) df-nf 1710 changed. (Revised by Wolf Lammen, 4-Oct-2021.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nfntOLDOLD  |-  ( F/ x ph  ->  F/ x  -.  ph )

Proof of Theorem nfntOLDOLD
StepHypRef Expression
1 notnot 136 . . . . 5  |-  ( ph  ->  -.  -.  ph )
21alimi 1739 . . . 4  |-  ( A. x ph  ->  A. x  -.  -.  ph )
32orim1i 539 . . 3  |-  ( ( A. x ph  \/  A. x  -.  ph )  ->  ( A. x  -.  -.  ph  \/  A. x  -.  ph ) )
4 pm1.4 401 . . 3  |-  ( ( A. x  -.  -.  ph  \/  A. x  -.  ph )  ->  ( A. x  -.  ph  \/  A. x  -.  -.  ph ) )
53, 4syl 17 . 2  |-  ( ( A. x ph  \/  A. x  -.  ph )  ->  ( A. x  -.  ph  \/  A. x  -.  -.  ph ) )
6 nf3 1712 . 2  |-  ( F/ x ph  <->  ( A. x ph  \/  A. x  -.  ph ) )
7 nf3 1712 . 2  |-  ( F/ x  -.  ph  <->  ( A. x  -.  ph  \/  A. x  -.  -.  ph ) )
85, 6, 73imtr4i 281 1  |-  ( F/ 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  ax-gen 1722  ax-4 1737
This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710
This theorem is referenced by: (None)
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