Theorem bnj105 34880

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 5329	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2832	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2113  Vcvv 3440  ∅c0 4285  {csn 4580  1_oc1o 8390

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708  ax-sep 5241  ax-nul 5251  ax-pow 5310

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-pw 4556  df-sn 4581  df-suc 6323  df-1o 8397

This theorem is referenced by:  bnj106  35024  bnj118  35025  bnj121  35026  bnj125  35028  bnj130  35030  bnj153  35036