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Theorem neeq2i 2614
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 2612 . 2  |-  ( A  =  B  ->  ( C  =/=  A  <->  C  =/=  B ) )
31, 2ax-mp 5 1  |-  ( C  =/=  A  <->  C  =/=  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    = wceq 1653    =/= wne 2601
This theorem is referenced by:  neeq12i  2615  neeqtri  2624  divnumden2  24166  nosgnn0  25618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-cleq 2431  df-ne 2603
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