Theorem bnj105 30790

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj105	|- 1o e. _V

Proof of Theorem bnj105

Step	Hyp	Ref	Expression
1		df1o2 7572	. 2 |- 1o = { (/) }
2		p0ex 4853	. 2 |- { (/) } e. _V
3	1, 2	eqeltri 2697	1 |- 1o e. _V

Syntax hints:   e. wcel 1990   _Vcvv 3200   (/)c0 3915   {csn 4177   1oc1o 7553

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-nul 4789  ax-pow 4843

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  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-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-pw 4160  df-sn 4178  df-suc 5729  df-1o 7560

This theorem is referenced by:  bnj106  30938  bnj118  30939  bnj121  30940  bnj125  30942  bnj130  30944  bnj153  30950