Theorem bnj105 32603

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 8279	. 2 ⊢ 1o = {∅}
2		p0ex 5302	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2835	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2108  Vcvv 3422  ∅c0 4253  {csn 4558  1_oc1o 8260

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-sep 5218  ax-nul 5225  ax-pow 5283

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4254  df-pw 4532  df-sn 4559  df-suc 6257  df-1o 8267

This theorem is referenced by:  bnj106  32748  bnj118  32749  bnj121  32750  bnj125  32752  bnj130  32754  bnj153  32760