MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  neor Structured version   Unicode version

Theorem neor 2727
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 368 . 2  |-  ( ( A  =  B  \/  ps )  <->  ( -.  A  =  B  ->  ps )
)
2 df-ne 2600 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
32imbi1i 323 . 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 366    = wceq 1405    =/= wne 2598
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 368  df-ne 2600
This theorem is referenced by:  fimaxre  10530  prime  10984  h1datomi  26913  elat2  27672  bnj563  29127  divrngidl  31707  dmncan1  31755  lkrshp4  32126  cvrcmp  32301  leat2  32312  isat3  32325  2llnmat  32541  2lnat  32801
  Copyright terms: Public domain W3C validator