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Theorem sneqi 3415
 Description: Equality inference for singletons. (Contributed by NM, 22-Jan-2004.)
Hypothesis
Ref Expression
sneqi.1 𝐴 = 𝐵
Assertion
Ref Expression
sneqi {𝐴} = {𝐵}

Proof of Theorem sneqi
StepHypRef Expression
1 sneqi.1 . 2 𝐴 = 𝐵
2 sneq 3414 . 2 (𝐴 = 𝐵 → {𝐴} = {𝐵})
31, 2ax-mp 7 1 {𝐴} = {𝐵}
 Colors of variables: wff set class Syntax hints:   = wceq 1259  {csn 3403 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-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-sn 3409 This theorem is referenced by:  fnressn  5377  fressnfv  5378  snriota  5525  xpassen  6335
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