Theorem bnj105 35058

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 8460	. 2 ⊢ 1o = {∅}
2		p0ex 5356	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2865	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2149  Vcvv 3461  ∅c0 4292  {csn 4592  1_oc1o 8446

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-sep 5259  ax-nul 5271  ax-pow 5337

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3463  df-dif 3914  df-un 3916  df-ss 3928  df-nul 4293  df-pw 4567  df-sn 4593  df-suc 6367  df-1o 8453

This theorem is referenced by:  bnj106  35201  bnj118  35202  bnj121  35203  bnj125  35205  bnj130  35207  bnj153  35213