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Theorem tsk1 10802
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 8512 . 2 1o = {∅}
2 tsk0 10801 . . 3 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → ∅ ∈ 𝑇)
3 tsksn 10798 . . 3 ((𝑇 ∈ Tarski ∧ ∅ ∈ 𝑇) → {∅} ∈ 𝑇)
42, 3syldan 591 . 2 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → {∅} ∈ 𝑇)
51, 4eqeltrid 2843 1 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → 1o𝑇)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wcel 2106  wne 2938  c0 4339  {csn 4631  1oc1o 8498  Tarskictsk 10786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-pow 5371
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-pw 4607  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149  df-suc 6392  df-1o 8505  df-tsk 10787
This theorem is referenced by:  tsk2  10803
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