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Theorem neeq2i 2457
Description: Inference for inequality. (Contributed by NM, 29-Apr-2005.)
Hypothesis
Ref Expression
neeq1i.1  |-  A  =  B
Assertion
Ref Expression
neeq2i  |-  ( C  =/=  A  <->  C  =/=  B )

Proof of Theorem neeq2i
StepHypRef Expression
1 neeq1i.1 . 2  |-  A  =  B
2 neeq2 2455 . 2  |-  ( A  =  B  ->  ( C  =/=  A  <->  C  =/=  B ) )
31, 2ax-mp 8 1  |-  ( C  =/=  A  <->  C  =/=  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1623    =/= wne 2446
This theorem is referenced by:  neeq12i  2458  neeqtri  2467  nosgnn0  24312
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-cleq 2276  df-ne 2448
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