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Theorem neeq12i 2326
Description: Inference for inequality. (Contributed by NM, 24-Jul-2012.)
Hypotheses
Ref Expression
neeq1i.1  |-  A  =  B
neeq12i.2  |-  C  =  D
Assertion
Ref Expression
neeq12i  |-  ( A  =/=  C  <->  B  =/=  D )

Proof of Theorem neeq12i
StepHypRef Expression
1 neeq12i.2 . . 3  |-  C  =  D
21neeq2i 2325 . 2  |-  ( A  =/=  C  <->  A  =/=  D )
3 neeq1i.1 . . 3  |-  A  =  B
43neeq1i 2324 . 2  |-  ( A  =/=  D  <->  B  =/=  D )
52, 4bitri 183 1  |-  ( A  =/=  C  <->  B  =/=  D )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1332    =/= wne 2309
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1424  ax-gen 1426  ax-4 1488  ax-17 1507  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-cleq 2133  df-ne 2310
This theorem is referenced by:  3netr3g  2343  3netr4g  2344  setsmsbasg  12678  setsmsdsg  12679
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