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Theorem enpr1g 9017
Description: {𝐴, 𝐴} has only one element. (Contributed by FL, 15-Feb-2010.)
Assertion
Ref Expression
enpr1g (𝐴𝑉 → {𝐴, 𝐴} ≈ 1o)

Proof of Theorem enpr1g
StepHypRef Expression
1 dfsn2 4634 . 2 {𝐴} = {𝐴, 𝐴}
2 ensn1g 9016 . 2 (𝐴𝑉 → {𝐴} ≈ 1o)
31, 2eqbrtrrid 5175 1 (𝐴𝑉 → {𝐴, 𝐴} ≈ 1o)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  {csn 4621  {cpr 4623   class class class wbr 5139  1oc1o 8455  cen 8933
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-mo 2526  df-clab 2702  df-cleq 2716  df-clel 2802  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-br 5140  df-opab 5202  df-id 5565  df-xp 5673  df-rel 5674  df-cnv 5675  df-co 5676  df-dm 5677  df-rn 5678  df-suc 6361  df-fun 6536  df-fn 6537  df-f 6538  df-f1 6539  df-fo 6540  df-f1o 6541  df-1o 8462  df-en 8937
This theorem is referenced by:  pr2neOLD  9997
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