Theorem bnj105 35122

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 8458	. 2 ⊢ 1o = {∅}
2		p0ex 5354	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2858	1 ⊢ 1o ∈ V

This proof depends on syntax axioms:   ∈ wcel 2142  Vcvv 3454  ∅c0 4285  {csn 4588  1_oc1o 8444

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734  ax-sep 5256  ax-nul 5268  ax-pow 5335

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1572  df-fal 1582  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-dif 3907  df-un 3909  df-ss 3921  df-nul 4286  df-pw 4563  df-sn 4589  df-suc 6366  df-1o 8451

This theorem is used by:  bnj106  35265  bnj118  35266  bnj121  35267  bnj125  35269  bnj130  35271  bnj153  35277