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Theorem preq2i 3887
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 3884 . 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 1652   {cpr 3815
This theorem is referenced by:  opid  4002  funopg  5485  df2o2  6738  fzprval  11106  fzo0to2pr  11184  fzo0to42pr  11186  prmreclem2  13285  txindis  17666  iblcnlem1  19679  usgraexvlem  21414  wlkntrllem2  21560  constr1trl  21588  constr3trllem3  21639  constr3pthlem1  21642  constr3pthlem3  21644  axlowdimlem4  25884  bpoly3  26104
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-sn 3820  df-pr 3821
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