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Theorem tsk1 8402
Description: One is an element of a non-empty Tarski's class. (Contributed by FL, 22-Feb-2011.)
Assertion
Ref Expression
tsk1  |-  ( ( T  e.  Tarski  /\  T  =/=  (/) )  ->  1o  e.  T )

Proof of Theorem tsk1
StepHypRef Expression
1 df1o2 6507 . 2  |-  1o  =  { (/) }
2 tsk0 8401 . . 3  |-  ( ( T  e.  Tarski  /\  T  =/=  (/) )  ->  (/)  e.  T
)
3 tsksn 8398 . . 3  |-  ( ( T  e.  Tarski  /\  (/)  e.  T
)  ->  { (/) }  e.  T )
42, 3syldan 456 . 2  |-  ( ( T  e.  Tarski  /\  T  =/=  (/) )  ->  { (/) }  e.  T )
51, 4syl5eqel 2380 1  |-  ( ( T  e.  Tarski  /\  T  =/=  (/) )  ->  1o  e.  T )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1696    =/= wne 2459   (/)c0 3468   {csn 3653   1oc1o 6488   Tarskictsk 8386
This theorem is referenced by:  tsk2  8403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-pow 4204
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-pw 3640  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-suc 4414  df-1o 6495  df-tsk 8387
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