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Theorem enpr1g 9016
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 4633 . 2 {𝐴} = {𝐴, 𝐴}
2 ensn1g 9015 . 2 (𝐴𝑉 → {𝐴} ≈ 1o)
31, 2eqbrtrrid 5174 1 (𝐴𝑉 → {𝐴, 𝐴} ≈ 1o)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  {csn 4620  {cpr 4622   class class class wbr 5138  1oc1o 8454  cen 8932
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 5289  ax-nul 5296  ax-pr 5417
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 3943  df-un 3945  df-in 3947  df-ss 3957  df-nul 4315  df-if 4521  df-sn 4621  df-pr 4623  df-op 4627  df-br 5139  df-opab 5201  df-id 5564  df-xp 5672  df-rel 5673  df-cnv 5674  df-co 5675  df-dm 5676  df-rn 5677  df-suc 6360  df-fun 6535  df-fn 6536  df-f 6537  df-f1 6538  df-fo 6539  df-f1o 6540  df-1o 8461  df-en 8936
This theorem is referenced by:  pr2neOLD  9996
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