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Theorem neeq2i 2997
 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 2772 . 2 (𝐶 = 𝐴𝐶 = 𝐵)
32necon3bii 2984 1 (𝐶𝐴𝐶𝐵)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196   = wceq 1632   ≠ wne 2932 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-cleq 2753  df-ne 2933 This theorem is referenced by:  neeqtri  3004  suppvalbr  7467  upgr3v3e3cycl  27332  upgr4cycl4dv4e  27337  disjdsct  29789  divnumden2  29873  nosgnn0  32117
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