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Theorem tsk1 10179
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 8103 . 2 1o = {∅}
2 tsk0 10178 . . 3 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → ∅ ∈ 𝑇)
3 tsksn 10175 . . 3 ((𝑇 ∈ Tarski ∧ ∅ ∈ 𝑇) → {∅} ∈ 𝑇)
42, 3syldan 594 . 2 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → {∅} ∈ 𝑇)
51, 4eqeltrid 2897 1 ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → 1o𝑇)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wcel 2112  wne 2990  c0 4246  {csn 4528  1oc1o 8082  Tarskictsk 10163
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 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-sep 5170  ax-pow 5234
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 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-ne 2991  df-ral 3114  df-rex 3115  df-rab 3118  df-v 3446  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4247  df-pw 4502  df-sn 4529  df-pr 4531  df-op 4535  df-br 5034  df-suc 6169  df-1o 8089  df-tsk 10164
This theorem is referenced by:  tsk2  10180
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