Theorem bnj105 35022

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 8446	. 2 ⊢ 1o = {∅}
2		p0ex 5343	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2860	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2144  Vcvv 3456  ∅c0 4287  {csn 4584  1_oc1o 8432

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-ext 2736  ax-sep 5248  ax-nul 5258  ax-pow 5324

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1565  df-fal 1575  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-v 3458  df-dif 3909  df-un 3911  df-ss 3923  df-nul 4288  df-pw 4559  df-sn 4585  df-suc 6354  df-1o 8439

This theorem is referenced by:  bnj106  35165  bnj118  35166  bnj121  35167  bnj125  35169  bnj130  35171  bnj153  35177