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Theorem neeq2i 3033
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 2791 . 2 (𝐶 = 𝐴𝐶 = 𝐵)
32necon3bii 3020 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 198   = wceq 1507  wne 2968
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-9 2059  ax-ext 2751
This theorem depends on definitions:  df-bi 199  df-an 388  df-ex 1743  df-cleq 2772  df-ne 2969
This theorem is referenced by:  neeqtri  3040  suppvalbr  7637  upgr3v3e3cycl  27709  upgr4cycl4dv4e  27714  disjdsct  30190  divnumden2  30280  nosgnn0  32683
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