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Theorem difprsn2 3495
Description: Removal of a singleton from an unordered pair. (Contributed by Alexander van der Vekens, 5-Oct-2017.)
Assertion
Ref Expression
difprsn2  =/=  { ,  }  \  { }  { }

Proof of Theorem difprsn2
StepHypRef Expression
1 prcom 3437 . . 3  { ,  }  { ,  }
21difeq1i 3052 . 2  { ,  }  \  { }  { ,  }  \  { }
3 necom 2283 . . 3  =/=  =/=
4 difprsn1 3494 . . 3  =/=  { ,  }  \  { }  { }
53, 4sylbi 114 . 2  =/=  { ,  }  \  { }  { }
62, 5syl5eq 2081 1  =/=  { ,  }  \  { }  { }
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242    =/= wne 2201    \ cdif 2908   {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-ne 2203  df-ral 2305  df-rab 2309  df-v 2553  df-dif 2914  df-un 2916  df-in 2918  df-ss 2925  df-nul 3219  df-sn 3373  df-pr 3374
This theorem is referenced by: (None)
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