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Theorem syl5eqner 2282
Description: B chained equality inference for inequality. (Contributed by NM, 6-Jun-2012.)
Hypotheses
Ref Expression
syl5eqner.1 𝐵 = 𝐴
syl5eqner.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
syl5eqner (𝜑𝐴𝐶)

Proof of Theorem syl5eqner
StepHypRef Expression
1 syl5eqner.2 . 2 (𝜑𝐵𝐶)
2 syl5eqner.1 . . 3 𝐵 = 𝐴
32neeq1i 2266 . 2 (𝐵𝐶𝐴𝐶)
41, 3sylib 120 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287  wne 2251
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1379  ax-gen 1381  ax-4 1443  ax-17 1462  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-cleq 2078  df-ne 2252
This theorem is referenced by: (None)
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