Theorem bnj105 35355

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 8483	. 2 ⊢ 1o = {∅}
2		p0ex 5345	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2856	1 ⊢ 1o ∈ V

This proof depends on syntax axioms:   ∈ wcel 2144  Vcvv 3450  ∅c0 4278  {csn 4583  1_oc1o 8469

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-sep 5248  ax-nul 5259  ax-pow 5326

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-dif 4047  df-un 4151  df-nul 4279  df-pw 4558  df-sn 4584  df-suc 6368  df-1o 8476

This theorem is used by:  bnj106  35498  bnj118  35499  bnj121  35500  bnj125  35502  bnj130  35504  bnj153  35510