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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  11927  strle1g  12059
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