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Theorem neeq2i 3006
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 2750 . 2 (𝐶 = 𝐴𝐶 = 𝐵)
32necon3bii 2993 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 209   = wceq 1543  wne 2940
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-9 2120  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788  df-cleq 2729  df-ne 2941
This theorem is referenced by:  neeqtri  3013  omsucne  7663  suppvalbr  7907  upgr3v3e3cycl  28263  upgr4cycl4dv4e  28268  disjdsct  30755  divnumden2  30852  usgrgt2cycl  32805  nosgnn0  33598
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