Theorem bnj105 34922

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 8406	. 2 ⊢ 1o = {∅}
2		p0ex 5316	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2837	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2121  Vcvv 3433  ∅c0 4264  {csn 4558  1_oc1o 8392

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-ext 2713  ax-sep 5221  ax-nul 5231  ax-pow 5297

This theorem depends on definitions:  df-bi 209  df-an 398  df-or 855  df-tru 1551  df-fal 1561  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-v 3435  df-dif 3888  df-un 3890  df-ss 3902  df-nul 4265  df-pw 4534  df-sn 4559  df-suc 6320  df-1o 8399

This theorem is referenced by:  bnj106  35065  bnj118  35066  bnj121  35067  bnj125  35069  bnj130  35071  bnj153  35077