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Theorem sneqi 3665
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 3664 . 2  |-  ( A  =  B  ->  { A }  =  { B } )
31, 2ax-mp 8 1  |-  { A }  =  { B }
Colors of variables: wff set class
Syntax hints:    = wceq 1632   {csn 3653
This theorem is referenced by:  fnressn  5721  fressnfv  5723  xpassen  6972  ids1  11453  strlemor1  13251  strle1  13255  ghmeqker  14725  pws1  15415  pwsmgp  15417  lpival  16013  imasdsf1olem  17953  ginvsn  21032  zrdivrng  21115  hh0oi  22499  vdgr1c  23911  dffv5  24534  bpoly3  24865  isdrngo1  26690  mapfzcons  26896  mapfzcons1  26897  mapfzcons2  26899  bnj601  29268
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-sn 3659
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