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Theorem prprc 3471
Description: An unordered pair containing two proper classes is the empty set. (Contributed by NM, 22-Mar-2006.)
Assertion
Ref Expression
prprc  _V  _V  { ,  }  (/)

Proof of Theorem prprc
StepHypRef Expression
1 prprc1 3469 . 2  _V  { ,  }  { }
2 snprc 3426 . . 3  _V  { }  (/)
32biimpi 113 . 2  _V  { }  (/)
41, 3sylan9eq 2089 1  _V  _V  { ,  }  (/)
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wceq 1242   wcel 1390   _Vcvv 2551   (/)c0 3218   {csn 3367   {cpr 3368
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-un 2916  df-nul 3219  df-sn 3373  df-pr 3374
This theorem is referenced by: (None)
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