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Theorem prprc2 3859
Description: A proper class vanishes in an unordered pair. (Contributed by NM, 22-Mar-2006.)
Assertion
Ref Expression
prprc2  |-  ( -.  B  e.  _V  ->  { A ,  B }  =  { A } )

Proof of Theorem prprc2
StepHypRef Expression
1 prcom 3826 . 2  |-  { A ,  B }  =  { B ,  A }
2 prprc1 3858 . 2  |-  ( -.  B  e.  _V  ->  { B ,  A }  =  { A } )
31, 2syl5eq 2432 1  |-  ( -.  B  e.  _V  ->  { A ,  B }  =  { A } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1649    e. wcel 1717   _Vcvv 2900   {csn 3758   {cpr 3759
This theorem is referenced by:  tpprceq3  3882  prex  4348  indislem  16988  usgraedgprv  21264  indispcon  24701  1to2vfriswmgra  27760
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-ne 2553  df-v 2902  df-dif 3267  df-un 3269  df-nul 3573  df-sn 3764  df-pr 3765
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