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Theorem sneqi 3583
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 3582 . 2  |-  ( A  =  B  ->  { A }  =  { B } )
31, 2ax-mp 5 1  |-  { A }  =  { B }
Colors of variables: wff set class
Syntax hints:    = wceq 1342   {csn 3571
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 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-11 1493  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-sn 3577
This theorem is referenced by:  fnressn  5666  fressnfv  5667  snriota  5822  xpassen  6788  ennnfonelem1  12303  strle1g  12447
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