Theorem bnj105 34721

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 8444	. 2 ⊢ 1o = {∅}
2		p0ex 5342	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2825	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2109  Vcvv 3450  ∅c0 4299  {csn 4592  1_oc1o 8430

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 2702  ax-sep 5254  ax-nul 5264  ax-pow 5323

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 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-dif 3920  df-un 3922  df-ss 3934  df-nul 4300  df-pw 4568  df-sn 4593  df-suc 6341  df-1o 8437

This theorem is referenced by:  bnj106  34865  bnj118  34866  bnj121  34867  bnj125  34869  bnj130  34871  bnj153  34877