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Theorem prprc2 3600
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 3567 . 2  |-  { A ,  B }  =  { B ,  A }
2 prprc1 3599 . 2  |-  ( -.  B  e.  _V  ->  { B ,  A }  =  { A } )
31, 2syl5eq 2160 1  |-  ( -.  B  e.  _V  ->  { A ,  B }  =  { A } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1314    e. wcel 1463   _Vcvv 2658   {csn 3495   {cpr 3496
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-dif 3041  df-un 3043  df-nul 3332  df-sn 3501  df-pr 3502
This theorem is referenced by: (None)
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