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Theorem neeq1i 2355
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 2353 . 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 104    = wceq 1348    =/= wne 2340
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 609  ax-in2 610  ax-5 1440  ax-gen 1442  ax-4 1503  ax-17 1519  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-cleq 2163  df-ne 2341
This theorem is referenced by:  neeq12i  2357  eqnetri  2363  eqnetrrid  2371  rabn0r  3441
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