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Theorem enpr1g 8550
 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 4553 . 2 {𝐴} = {𝐴, 𝐴}
2 ensn1g 8549 . 2 (𝐴𝑉 → {𝐴} ≈ 1o)
31, 2eqbrtrrid 5075 1 (𝐴𝑉 → {𝐴, 𝐴} ≈ 1o)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2115  {csn 4540  {cpr 4542   class class class wbr 5039  1oc1o 8070   ≈ cen 8481 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2178  ax-ext 2793  ax-sep 5176  ax-nul 5183  ax-pr 5303  ax-un 7436 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2623  df-eu 2654  df-clab 2800  df-cleq 2814  df-clel 2892  df-nfc 2960  df-ral 3131  df-rex 3132  df-rab 3135  df-v 3473  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4267  df-if 4441  df-sn 4541  df-pr 4543  df-op 4547  df-uni 4812  df-br 5040  df-opab 5102  df-id 5433  df-xp 5534  df-rel 5535  df-cnv 5536  df-co 5537  df-dm 5538  df-rn 5539  df-suc 6170  df-fun 6330  df-fn 6331  df-f 6332  df-f1 6333  df-fo 6334  df-f1o 6335  df-1o 8077  df-en 8485 This theorem is referenced by:  pr2ne  9408
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