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Theorem imsym1 26160
Description: A symmetry with  ->.

See negsym1 26159 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
imsym1  |-  ( ( ps  ->  ( ps  ->  F.  ) )  -> 
( ps  ->  ph )
)

Proof of Theorem imsym1
StepHypRef Expression
1 pm2.21 102 . 2  |-  ( -. 
ps  ->  ( ps  ->  ph ) )
2 falim 1337 . . 3  |-  (  F. 
->  ph )
32imim2i 14 . 2  |-  ( ( ps  ->  F.  )  ->  ( ps  ->  ph )
)
41, 3ja 155 1  |-  ( ( ps  ->  ( ps  ->  F.  ) )  -> 
( ps  ->  ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    F. wfal 1326
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 178  df-tru 1328  df-fal 1329
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