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Theorem prprc2 4728
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 4694 . 2 {𝐴, 𝐵} = {𝐵, 𝐴}
2 prprc1 4727 . 2 𝐵 ∈ V → {𝐵, 𝐴} = {𝐴})
31, 2eqtrid 2785 1 𝐵 ∈ V → {𝐴, 𝐵} = {𝐴})
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1542  wcel 2107  Vcvv 3444  {csn 4587  {cpr 4589
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-dif 3914  df-un 3916  df-nul 4284  df-sn 4588  df-pr 4590
This theorem is referenced by:  tpprceq3  4765  elpreqprlem  4824  prex  5390  indislem  22366  1to2vfriswmgr  29265  indispconn  33885  bj-prmoore  35632  elsprel  45753
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