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Theorem sneqi 3539
 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 3538 . 2 (𝐴 = 𝐵 → {𝐴} = {𝐵})
31, 2ax-mp 5 1 {𝐴} = {𝐵}
 Colors of variables: wff set class Syntax hints:   = wceq 1331  {csn 3527 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-sn 3533 This theorem is referenced by:  fnressn  5606  fressnfv  5607  snriota  5759  xpassen  6724  ennnfonelem1  11931  strle1g  12063
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