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Theorem neor 2791
Description: Logical OR with an equality. (Contributed by NM, 29-Apr-2007.)
Assertion
Ref Expression
neor  |-  ( ( A  =  B  \/  ps )  <->  ( A  =/= 
B  ->  ps )
)

Proof of Theorem neor
StepHypRef Expression
1 df-or 370 . 2  |-  ( ( A  =  B  \/  ps )  <->  ( -.  A  =  B  ->  ps )
)
2 df-ne 2664 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
32imbi1i 325 . 2  |-  ( ( A  =/=  B  ->  ps )  <->  ( -.  A  =  B  ->  ps )
)
41, 3bitr4i 252 1  |-  ( ( A  =  B  \/  ps )  <->  ( A  =/= 
B  ->  ps )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    \/ wo 368    = wceq 1379    =/= wne 2662
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 185  df-or 370  df-ne 2664
This theorem is referenced by:  fimaxre  10486  prime  10937  h1datomi  26175  elat2  26935  divrngidl  30028  dmncan1  30076  bnj563  32879  lkrshp4  33905  cvrcmp  34080  leat2  34091  isat3  34104  2llnmat  34320  2lnat  34580
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