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Theorem neeq1i 2235
Description: Inference for inequality. (Contributed by NM, 29-Apr-2005.)
Hypothesis
Ref Expression
neeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
neeq1i (𝐴𝐶𝐵𝐶)

Proof of Theorem neeq1i
StepHypRef Expression
1 neeq1i.1 . 2 𝐴 = 𝐵
2 neeq1 2233 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2ax-mp 7 1 (𝐴𝐶𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wb 102   = wceq 1259  wne 2220
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-ne 2221
This theorem is referenced by:  neeq12i  2237  eqnetri  2243  syl5eqner  2251  rabn0r  3272
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