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Theorem bj-nf3 33155
Description: Alternate definition of df-bj-nf 33153. (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-nf3  |-  (FF/ x
ph 
<->  ( A. x ph  \/  A. x  -.  ph ) )

Proof of Theorem bj-nf3
StepHypRef Expression
1 bj-nf2 33154 . 2  |-  (FF/ x
ph 
<->  ( A. x ph  \/  -.  E. x ph ) )
2 alnex 1593 . . . 4  |-  ( A. x  -.  ph  <->  -.  E. x ph )
32bicomi 202 . . 3  |-  ( -. 
E. x ph  <->  A. x  -.  ph )
43orbi2i 519 . 2  |-  ( ( A. x ph  \/  -.  E. x ph )  <->  ( A. x ph  \/  A. x  -.  ph )
)
51, 4bitri 249 1  |-  (FF/ x
ph 
<->  ( A. x ph  \/  A. x  -.  ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ wo 368   A.wal 1372   E.wex 1591  FF/wnff 33152
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 185  df-or 370  df-ex 1592  df-bj-nf 33153
This theorem is referenced by:  bj-nfntht2  33158  bj-nfn  33182
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