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Theorem neeq2i 2711
Description: Inference for inequality. (Contributed by NM, 29-Apr-2005.) (Proof shortened by Wolf Lammen, 19-Nov-2019.)
Hypothesis
Ref Expression
neeq1i.1  |-  A  =  B
Assertion
Ref Expression
neeq2i  |-  ( C  =/=  A  <->  C  =/=  B )

Proof of Theorem neeq2i
StepHypRef Expression
1 neeq1i.1 . . 3  |-  A  =  B
21eqeq2i 2440 . 2  |-  ( C  =  A  <->  C  =  B )
32necon3bii 2692 1  |-  ( C  =/=  A  <->  C  =/=  B )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    = wceq 1437    =/= wne 2618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-cleq 2414  df-ne 2620
This theorem is referenced by:  neeq12iOLD  2714  neeqtri  2722  suppvalbr  6926  disjdsct  28273  divnumden2  28376  nosgnn0  30540
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