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Theorem prprc2 4766
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 4732 . 2 {𝐴, 𝐵} = {𝐵, 𝐴}
2 prprc1 4765 . 2 𝐵 ∈ V → {𝐵, 𝐴} = {𝐴})
31, 2eqtrid 2789 1 𝐵 ∈ V → {𝐴, 𝐵} = {𝐴})
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1540  wcel 2108  Vcvv 3480  {csn 4626  {cpr 4628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-dif 3954  df-un 3956  df-nul 4334  df-sn 4627  df-pr 4629
This theorem is referenced by:  tpprceq3  4804  elpreqprlem  4866  prex  5437  prfi  9363  indislem  23007  1to2vfriswmgr  30298  indispconn  35239  bj-prmoore  37116  elsprel  47462
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