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Theorem bisym1 24858
Description: A symmetry with  <->.

See negsym1 24856 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
bisym1  |-  ( ( ps  <->  ( ps  <->  F.  )
)  ->  ( ps  <->  ph ) )

Proof of Theorem bisym1
StepHypRef Expression
1 nbfal 1316 . . 3  |-  ( -. 
ps 
<->  ( ps  <->  F.  )
)
21bibi2i 304 . 2  |-  ( ( ps  <->  -.  ps )  <->  ( ps  <->  ( ps  <->  F.  )
) )
3 pm5.19 349 . . 3  |-  -.  ( ps 
<->  -.  ps )
43pm2.21i 123 . 2  |-  ( ( ps  <->  -.  ps )  ->  ( ps  <->  ph ) )
52, 4sylbir 204 1  |-  ( ( ps  <->  ( ps  <->  F.  )
)  ->  ( ps  <->  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    F. wfal 1308
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-fal 1311
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