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Theorem consym1 24859
Description: A symmetry with  /\.

See negsym1 24856 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 1319 . . 3  |-  (  F. 
->  ( ( ps  /\  ( ps  /\  F.  )
)  ->  ( ps  /\ 
ph ) ) )
21ad2antll 709 . 2  |-  ( ( ps  /\  ( ps 
/\  F.  ) )  ->  ( ( ps  /\  ( ps  /\  F.  )
)  ->  ( ps  /\ 
ph ) ) )
32pm2.43i 43 1  |-  ( ( ps  /\  ( ps 
/\  F.  ) )  ->  ( ps  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    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-an 360  df-tru 1310  df-fal 1311
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