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Theorem tsk1 10781
Description: One is an element of a nonempty Tarski class. (Contributed by FL, 22-Feb-2011.)
Assertion
Ref Expression
tsk1 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → 1o𝑇)

Proof of Theorem tsk1
StepHypRef Expression
1 df1o2 8487 . 2 1o = {∅}
2 tsk0 10780 . . 3 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → ∅ ∈ 𝑇)
3 tsksn 10777 . . 3 ((𝑇 ∈ Tarski ∧ ∅ ∈ 𝑇) → {∅} ∈ 𝑇)
42, 3syldan 590 . 2 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → {∅} ∈ 𝑇)
51, 4eqeltrid 2833 1 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → 1o𝑇)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wcel 2099  wne 2936  c0 4318  {csn 4624  1oc1o 8473  Tarskictsk 10765
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-10 2130  ax-12 2167  ax-ext 2699  ax-sep 5293  ax-pow 5359
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-nf 1779  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2937  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3472  df-dif 3948  df-un 3950  df-in 3952  df-ss 3962  df-nul 4319  df-if 4525  df-pw 4600  df-sn 4625  df-pr 4627  df-op 4631  df-br 5143  df-suc 6369  df-1o 8480  df-tsk 10766
This theorem is referenced by:  tsk2  10782
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