Theorem bnj105 34707

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 8418	. 2 ⊢ 1o = {∅}
2		p0ex 5334	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2824	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2109  Vcvv 3444  ∅c0 4292  {csn 4585  1_oc1o 8404

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-sep 5246  ax-nul 5256  ax-pow 5315

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3446  df-dif 3914  df-un 3916  df-ss 3928  df-nul 4293  df-pw 4561  df-sn 4586  df-suc 6326  df-1o 8411

This theorem is referenced by:  bnj106  34851  bnj118  34852  bnj121  34853  bnj125  34855  bnj130  34857  bnj153  34863