Theorem bnj105 32104

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 8099	. 2 ⊢ 1o = {∅}
2		p0ex 5250	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2886	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2111  Vcvv 3441  ∅c0 4243  {csn 4525  1_oc1o 8078

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5167  ax-nul 5174  ax-pow 5231

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-dif 3884  df-un 3886  df-in 3888  df-ss 3898  df-nul 4244  df-pw 4499  df-sn 4526  df-suc 6165  df-1o 8085

This theorem is referenced by:  bnj106  32250  bnj118  32251  bnj121  32252  bnj125  32254  bnj130  32256  bnj153  32262