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Theorem prprc2 3737
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 3705 . 2  |-  { A ,  B }  =  { B ,  A }
2 prprc1 3736 . 2  |-  ( -.  B  e.  _V  ->  { B ,  A }  =  { A } )
31, 2syl5eq 2327 1  |-  ( -.  B  e.  _V  ->  { A ,  B }  =  { A } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1623    e. wcel 1684   _Vcvv 2788   {csn 3640   {cpr 3641
This theorem is referenced by:  prex  4217  indislem  16737  indispcon  23176  tpprceq3  27483  usgraedgprv  27521  1to2vfriswmgra  27546
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-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-nul 3456  df-sn 3646  df-pr 3647
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