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Theorem prprc2 3713
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 3680 . 2 {𝐴, 𝐵} = {𝐵, 𝐴}
2 prprc1 3712 . 2 𝐵 ∈ V → {𝐵, 𝐴} = {𝐴})
31, 2eqtrid 2232 1 𝐵 ∈ V → {𝐴, 𝐵} = {𝐴})
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1363  wcel 2158  Vcvv 2749  {csn 3604  {cpr 3605
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-dif 3143  df-un 3145  df-nul 3435  df-sn 3610  df-pr 3611
This theorem is referenced by: (None)
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