Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dissym1 Structured version   Visualization version   Unicode version

Theorem dissym1 32420
Description: A symmetry with  \/.

See negsym1 32416 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
dissym1  |-  ( ( ps  \/  ( ps  \/ F.  ) )  ->  ( ps  \/  ph ) )

Proof of Theorem dissym1
StepHypRef Expression
1 orc 400 . 2  |-  ( ps 
->  ( ps  \/  ph ) )
2 falim 1498 . . 3  |-  ( F. 
->  ph )
32orim2i 540 . 2  |-  ( ( ps  \/ F.  )  ->  ( ps  \/  ph ) )
41, 3jaoi 394 1  |-  ( ( ps  \/  ( ps  \/ F.  ) )  ->  ( ps  \/  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 383   F. wfal 1488
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 197  df-or 385  df-tru 1486  df-fal 1489
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator