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Theorem preq2i 3723
Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012.)
Hypothesis
Ref Expression
preq1i.1  |-  A  =  B
Assertion
Ref Expression
preq2i  |-  { C ,  A }  =  { C ,  B }

Proof of Theorem preq2i
StepHypRef Expression
1 preq1i.1 . 2  |-  A  =  B
2 preq2 3720 . 2  |-  ( A  =  B  ->  { C ,  A }  =  { C ,  B }
)
31, 2ax-mp 8 1  |-  { C ,  A }  =  { C ,  B }
Colors of variables: wff set class
Syntax hints:    = wceq 1632   {cpr 3654
This theorem is referenced by:  opid  3830  funopg  5302  df2o2  6509  fzprval  10860  bitsinv1lem  12648  prmreclem2  12980  txindis  17344  iblcnlem1  19158  axlowdimlem4  24645  bpoly3  24865  intset  26147  fzo0to42pr  28211  usgraexvlem  28261  wlkntrllem1  28345  wlkntrllem4  28348  usgrcyclnl2  28387  constr3trllem3  28398  constr3pthlem1  28401  constr3pthlem3  28403
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-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-pr 3660
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