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Theorem neorian 2704
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 2613 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
2 df-ne 2613 . . 3  |-  ( C  =/=  D  <->  -.  C  =  D )
31, 2orbi12i 521 . 2  |-  ( ( A  =/=  B  \/  C  =/=  D )  <->  ( -.  A  =  B  \/  -.  C  =  D
) )
4 ianor 488 . 2  |-  ( -.  ( A  =  B  /\  C  =  D )  <->  ( -.  A  =  B  \/  -.  C  =  D )
)
53, 4bitr4i 252 1  |-  ( ( A  =/=  B  \/  C  =/=  D )  <->  -.  ( A  =  B  /\  C  =  D )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ wo 368    /\ wa 369    = wceq 1369    =/= wne 2611
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-an 371  df-ne 2613
This theorem is referenced by:  oeoa  7041  wemapso2OLD  7771  wemapso2lem  7772  recextlem2  9972  crne0  10320  crreczi  11994  gcdcllem3  13702  bezoutlem2  13728  dsmmacl  18171  txhaus  19225  itg1addlem2  21180  coeaddlem  21721  dcubic  22246
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