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Theorem preq2i 3710
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 3707 . 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 1623   {cpr 3641
This theorem is referenced by:  opid  3814  funopg  5286  df2o2  6493  fzprval  10844  bitsinv1lem  12632  prmreclem2  12964  txindis  17328  iblcnlem1  19142  axlowdimlem4  24573  bpoly3  24793  intset  26044  usgraexvlem  28127
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-sn 3646  df-pr 3647
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