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Theorem neorian 2533
Description: A DeMorgan'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 2448 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
2 df-ne 2448 . . 3  |-  ( C  =/=  D  <->  -.  C  =  D )
31, 2orbi12i 507 . 2  |-  ( ( A  =/=  B  \/  C  =/=  D )  <->  ( -.  A  =  B  \/  -.  C  =  D
) )
4 ianor 474 . 2  |-  ( -.  ( A  =  B  /\  C  =  D )  <->  ( -.  A  =  B  \/  -.  C  =  D )
)
53, 4bitr4i 243 1  |-  ( ( A  =/=  B  \/  C  =/=  D )  <->  -.  ( A  =  B  /\  C  =  D )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358    = wceq 1623    =/= wne 2446
This theorem is referenced by:  oeoa  6595  wemapso2  7267  recextlem2  9399  crne0  9739  crreczi  11226  gcdcllem3  12692  bezoutlem2  12718  txhaus  17341  itg1addlem2  19052  coeaddlem  19630  dcubic  20142  dsmmacl  27207
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 177  df-or 359  df-an 360  df-ne 2448
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