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Theorem neeq2i 3003
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 2741 . 2 (𝐶 = 𝐴𝐶 = 𝐵)
32necon3bii 2990 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1534  wne 2937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1775  df-cleq 2720  df-ne 2938
This theorem is referenced by:  neeqtri  3010  omsucne  7889  suppvalbr  8169  nosgnn0  27604  upgr3v3e3cycl  30003  upgr4cycl4dv4e  30008  disjdsct  32495  divnumden2  32594  usgrgt2cycl  34740  onov0suclim  42703
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