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Theorem neorian 2685
Description: A De Morgan's law for inequality. (Contributed by NM, 18-May-2007.)
Assertion
Ref Expression
neorian  |-  ( ( A  =/=  B  \/  C  =/=  D )  <->  -.  ( A  =  B  /\  C  =  D )
)

Proof of Theorem neorian
StepHypRef Expression
1 df-ne 2600 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
2 df-ne 2600 . . 3  |-  ( C  =/=  D  <->  -.  C  =  D )
31, 2orbi12i 508 . 2  |-  ( ( A  =/=  B  \/  C  =/=  D )  <->  ( -.  A  =  B  \/  -.  C  =  D
) )
4 ianor 475 . 2  |-  ( -.  ( A  =  B  /\  C  =  D )  <->  ( -.  A  =  B  \/  -.  C  =  D )
)
53, 4bitr4i 244 1  |-  ( ( A  =/=  B  \/  C  =/=  D )  <->  -.  ( A  =  B  /\  C  =  D )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    \/ wo 358    /\ wa 359    = wceq 1652    =/= wne 2598
This theorem is referenced by:  oeoa  6832  wemapso2  7513  recextlem2  9645  crne0  9985  crreczi  11496  gcdcllem3  13005  bezoutlem2  13031  txhaus  17671  itg1addlem2  19581  coeaddlem  20159  dcubic  20678  dsmmacl  27175
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-or 360  df-an 361  df-ne 2600
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