Theorem bnj105 34882

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 5330	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2833	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3441  ∅c0 4286  {csn 4581  1_oc1o 8392

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5242  ax-nul 5252  ax-pow 5311

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3443  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4287  df-pw 4557  df-sn 4582  df-suc 6324  df-1o 8399

This theorem is referenced by:  bnj106  35026  bnj118  35027  bnj121  35028  bnj125  35030  bnj130  35032  bnj153  35038