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Theorem preq2i 4103
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 4100 . 2  |-  ( A  =  B  ->  { C ,  A }  =  { C ,  B }
)
31, 2ax-mp 5 1  |-  { C ,  A }  =  { C ,  B }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1374   {cpr 4022
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-v 3108  df-un 3474  df-sn 4021  df-pr 4023
This theorem is referenced by:  opid  4225  funopg  5611  df2o2  7134  fzprval  11729  fzo0to2pr  11856  fzo0to42pr  11858  prmreclem2  14283  m2detleiblem2  18890  txindis  19863  iblcnlem1  21922  axlowdimlem4  23917  usgraexvlem  24057  wlkntrllem2  24224  constr1trl  24252  constr3trllem3  24314  constr3pthlem1  24317  constr3pthlem3  24319  bpoly3  29383
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