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Theorem neeq2i 3052
 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 2811 . 2 (𝐶 = 𝐴𝐶 = 𝐵)
32necon3bii 3039 1 (𝐶𝐴𝐶𝐵)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   = wceq 1538   ≠ wne 2987 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2791  df-ne 2988 This theorem is referenced by:  neeqtri  3059  omsucne  7580  suppvalbr  7819  upgr3v3e3cycl  27972  upgr4cycl4dv4e  27977  disjdsct  30469  divnumden2  30567  usgrgt2cycl  32502  nosgnn0  33290
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