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Theorem tsk1 10174
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 8105 . 2 1o = {∅}
2 tsk0 10173 . . 3 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → ∅ ∈ 𝑇)
3 tsksn 10170 . . 3 ((𝑇 ∈ Tarski ∧ ∅ ∈ 𝑇) → {∅} ∈ 𝑇)
42, 3syldan 591 . 2 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → {∅} ∈ 𝑇)
51, 4eqeltrid 2914 1 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → 1o𝑇)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wcel 2105  wne 3013  c0 4288  {csn 4557  1oc1o 8084  Tarskictsk 10158
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790  ax-sep 5194  ax-pow 5257
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ne 3014  df-ral 3140  df-rex 3141  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-pw 4537  df-sn 4558  df-pr 4560  df-op 4564  df-br 5058  df-suc 6190  df-1o 8091  df-tsk 10159
This theorem is referenced by:  tsk2  10175
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