Theorem tsk1 9586

Description: One is an element of a nonempty Tarski class. (Contributed by FL, 22-Feb-2011.)

Assertion

Ref	Expression
tsk1	|- ( ( T e. Tarski /\ T =/= (/) ) -> 1o e. T )

Proof of Theorem tsk1

Step	Hyp	Ref	Expression
1		df1o2 7572	. 2 |- 1o = { (/) }
2		tsk0 9585	. . 3 |- ( ( T e. Tarski /\ T =/= (/) ) -> (/) e. T )
3		tsksn 9582	. . 3 |- ( ( T e. Tarski /\ (/) e. T ) -> { (/) } e. T )
4	2, 3	syldan 487	. 2 |- ( ( T e. Tarski /\ T =/= (/) ) -> { (/) } e. T )
5	1, 4	syl5eqel 2705	1 |- ( ( T e. Tarski /\ T =/= (/) ) -> 1o e. T )

Syntax hints:   -> wi 4   /\ wa 384   e. wcel 1990   =/= wne 2794   (/)c0 3915   {csn 4177   1oc1o 7553   Tarskictsk 9570

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-pow 4843

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ne 2795  df-ral 2917  df-rex 2918  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-pw 4160  df-sn 4178  df-pr 4180  df-op 4184  df-br 4654  df-suc 5729  df-1o 7560  df-tsk 9571

This theorem is referenced by:  tsk2  9587