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Theorem prprc2 3546
Description: A proper class vanishes in an unordered pair. (Contributed by NM, 22-Mar-2006.)
Assertion
Ref Expression
prprc2 𝐵 ∈ V → {𝐴, 𝐵} = {𝐴})

Proof of Theorem prprc2
StepHypRef Expression
1 prcom 3513 . 2 {𝐴, 𝐵} = {𝐵, 𝐴}
2 prprc1 3545 . 2 𝐵 ∈ V → {𝐵, 𝐴} = {𝐴})
31, 2syl5eq 2132 1 𝐵 ∈ V → {𝐴, 𝐵} = {𝐴})
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1289  wcel 1438  Vcvv 2619  {csn 3441  {cpr 3442
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 2999  df-un 3001  df-nul 3285  df-sn 3447  df-pr 3448
This theorem is referenced by: (None)
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