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Theorem neeq2d 2328
 Description: Deduction for inequality. (Contributed by NM, 25-Oct-1999.)
Hypothesis
Ref Expression
neeq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
neeq2d (𝜑 → (𝐶𝐴𝐶𝐵))

Proof of Theorem neeq2d
StepHypRef Expression
1 neeq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 neeq2 2323 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2syl 14 1 (𝜑 → (𝐶𝐴𝐶𝐵))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104   = wceq 1332   ≠ wne 2309 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1424  ax-gen 1426  ax-4 1488  ax-17 1507  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-cleq 2133  df-ne 2310 This theorem is referenced by:  neeq12d  2329  neeqtrd  2337  sqrt2irr  11910  ennnfonelemk  11983  ennnfoneleminc  11994  ennnfonelemex  11997  ennnfonelemnn0  12005  ennnfonelemr  12006
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