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Theorem prprc2 4665
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 4631 . 2 {𝐴, 𝐵} = {𝐵, 𝐴}
2 prprc1 4664 . 2 𝐵 ∈ V → {𝐵, 𝐴} = {𝐴})
31, 2syl5eq 2848 1 𝐵 ∈ V → {𝐴, 𝐵} = {𝐴})
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1538  wcel 2112  Vcvv 3444  {csn 4528  {cpr 4530
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-dif 3887  df-un 3889  df-nul 4247  df-sn 4529  df-pr 4531
This theorem is referenced by:  tpprceq3  4700  elpreqprlem  4759  prex  5301  indislem  21609  1to2vfriswmgr  28068  indispconn  32595  bj-prmoore  34531  elsprel  43989
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