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Theorem neor 2691
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 2603 . . 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 1369    =/= wne 2601
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 2603
This theorem is referenced by:  fimaxre  10269  prime  10714  h1datomi  24935  elat2  25695  divrngidl  28781  dmncan1  28829  bnj563  31622  lkrshp4  32593  cvrcmp  32768  leat2  32779  isat3  32792  2llnmat  33008  2lnat  33268
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