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Theorem neeq1i 2297
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 2295 . 2  |-  ( A  =  B  ->  ( A  =/=  C  <->  B  =/=  C ) )
31, 2ax-mp 7 1  |-  ( A  =/=  C  <->  B  =/=  C )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1314    =/= wne 2282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-4 1470  ax-17 1489  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2283
This theorem is referenced by:  neeq12i  2299  eqnetri  2305  syl5eqner  2313  rabn0r  3355
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