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Theorem neeq2d 2239
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 2234 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2syl 14 1 (𝜑 → (𝐶𝐴𝐶𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  neeq12d  2240  neeqtrd  2248  sqrt2irr  10251
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