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Theorem neeq1d 2267
Description: Deduction for inequality. (Contributed by NM, 25-Oct-1999.)
Hypothesis
Ref Expression
neeq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
neeq1d (𝜑 → (𝐴𝐶𝐵𝐶))

Proof of Theorem neeq1d
StepHypRef Expression
1 neeq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 neeq1 2262 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2syl 14 1 (𝜑 → (𝐴𝐶𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103   = wceq 1285  wne 2249
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 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250
This theorem is referenced by:  neeq12d  2269  eqnetrd  2273  prnzg  3532  hashprg  9884  ialgcvg  10637  ialgcvga  10640  eucialgcvga  10647  rpdvds  10688  phibndlem  10799  dfphi2  10803
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