Theorem bnj105 34859

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 8404	. 2 ⊢ 1o = {∅}
2		p0ex 5328	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2831	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3439  ∅c0 4284  {csn 4579  1_oc1o 8390

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 2707  ax-sep 5240  ax-nul 5250  ax-pow 5309

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 2714  df-cleq 2727  df-clel 2810  df-v 3441  df-dif 3903  df-un 3905  df-ss 3917  df-nul 4285  df-pw 4555  df-sn 4580  df-suc 6322  df-1o 8397

This theorem is referenced by:  bnj106  35003  bnj118  35004  bnj121  35005  bnj125  35007  bnj130  35009  bnj153  35015