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Theorem neeq2i 3081
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 (𝐶𝐴𝐶𝐵)

Proof of Theorem neeq2i
StepHypRef Expression
1 neeq1i.1 . . 3 𝐴 = 𝐵
21eqeq2i 2834 . 2 (𝐶 = 𝐴𝐶 = 𝐵)
32necon3bii 3068 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 207   = wceq 1528  wne 3016
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-9 2115  ax-ext 2793
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-cleq 2814  df-ne 3017
This theorem is referenced by:  neeqtri  3088  omsucne  7586  suppvalbr  7825  upgr3v3e3cycl  27887  upgr4cycl4dv4e  27892  disjdsct  30365  divnumden2  30461  usgrgt2cycl  32275  nosgnn0  33063
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