Theorem bnj105 34716

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 8511	. 2 ⊢ 1o = {∅}
2		p0ex 5389	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2834	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2105  Vcvv 3477  ∅c0 4338  {csn 4630  1_oc1o 8497

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705  ax-sep 5301  ax-nul 5311  ax-pow 5370

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-dif 3965  df-un 3967  df-ss 3979  df-nul 4339  df-pw 4606  df-sn 4631  df-suc 6391  df-1o 8504

This theorem is referenced by:  bnj106  34860  bnj118  34861  bnj121  34862  bnj125  34864  bnj130  34866  bnj153  34872