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Theorem enpr1g 9045
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 4642 . 2 {𝐴} = {𝐴, 𝐴}
2 ensn1g 9044 . 2 (𝐴𝑉 → {𝐴} ≈ 1o)
31, 2eqbrtrrid 5184 1 (𝐴𝑉 → {𝐴, 𝐴} ≈ 1o)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2099  {csn 4629  {cpr 4631   class class class wbr 5148  1oc1o 8480  cen 8961
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-sep 5299  ax-nul 5306  ax-pr 5429
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-mo 2530  df-clab 2706  df-cleq 2720  df-clel 2806  df-ral 3059  df-rex 3068  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-br 5149  df-opab 5211  df-id 5576  df-xp 5684  df-rel 5685  df-cnv 5686  df-co 5687  df-dm 5688  df-rn 5689  df-suc 6375  df-fun 6550  df-fn 6551  df-f 6552  df-f1 6553  df-fo 6554  df-f1o 6555  df-1o 8487  df-en 8965
This theorem is referenced by:  pr2neOLD  10029
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