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Theorem consym1 26175
Description: A symmetry with  /\.

See negsym1 26172 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
consym1  |-  ( ( ps  /\  ( ps 
/\  F.  ) )  ->  ( ps  /\  ph ) )

Proof of Theorem consym1
StepHypRef Expression
1 falim 1338 . . 3  |-  (  F. 
->  ( ( ps  /\  ( ps  /\  F.  )
)  ->  ( ps  /\ 
ph ) ) )
21ad2antll 711 . 2  |-  ( ( ps  /\  ( ps 
/\  F.  ) )  ->  ( ( ps  /\  ( ps  /\  F.  )
)  ->  ( ps  /\ 
ph ) ) )
32pm2.43i 46 1  |-  ( ( ps  /\  ( ps 
/\  F.  ) )  ->  ( ps  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    F. wfal 1327
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 179  df-an 362  df-tru 1329  df-fal 1330
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