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Theorem neeq1i 2372
Description: Inference for inequality. (Contributed by NM, 29-Apr-2005.)
Hypothesis
Ref Expression
neeq1i.1  |-  A  =  B
Assertion
Ref Expression
neeq1i  |-  ( A  =/=  C  <->  B  =/=  C )

Proof of Theorem neeq1i
StepHypRef Expression
1 neeq1i.1 . 2  |-  A  =  B
2 neeq1 2370 . 2  |-  ( A  =  B  ->  ( A  =/=  C  <->  B  =/=  C ) )
31, 2ax-mp 5 1  |-  ( A  =/=  C  <->  B  =/=  C )
Colors of variables: wff set class
Syntax hints:    <-> wb 105    = wceq 1363    =/= wne 2357
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1457  ax-gen 1459  ax-4 1520  ax-17 1536  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-cleq 2180  df-ne 2358
This theorem is referenced by:  neeq12i  2374  eqnetri  2380  eqnetrrid  2388  rabn0r  3461
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