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Theorem neeq2i 2700
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 2473 . 2  |-  ( C  =  A  <->  C  =  B )
32necon3bii 2687 1  |-  ( C  =/=  A  <->  C  =/=  B )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189    = wceq 1454    =/= wne 2632
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-ext 2441
This theorem depends on definitions:  df-bi 190  df-cleq 2454  df-ne 2634
This theorem is referenced by:  neeqtri  2707  suppvalbr  6944  disjdsct  28331  divnumden2  28429  nosgnn0  30593  upgr3v3e3cycl  39920  upgr4cycl4dv4e  39925
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