Theorem bnj105 34200

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

Assertion

Ref	Expression
bnj105	⊢ 1o ∈ V

Proof of Theorem bnj105

Step	Hyp	Ref	Expression
1		df1o2 8479	. 2 ⊢ 1o = {∅}
2		p0ex 5382	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2828	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2105  Vcvv 3473  ∅c0 4322  {csn 4628  1_oc1o 8465

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702  ax-sep 5299  ax-nul 5306  ax-pow 5363

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3475  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-pw 4604  df-sn 4629  df-suc 6370  df-1o 8472

This theorem is referenced by:  bnj106  34344  bnj118  34345  bnj121  34346  bnj125  34348  bnj130  34350  bnj153  34356