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Theorem neeq1i 2220
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 2218 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2ax-mp 7 1 (𝐴𝐶𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wb 98   = wceq 1243  wne 2204
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206
This theorem is referenced by:  neeq12i  2222  eqnetri  2228  syl5eqner  2236  rabn0r  3244
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