Theorem bnj105 31994

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 8116	. 2 ⊢ 1o = {∅}
2		p0ex 5285	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2909	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3494  ∅c0 4291  {csn 4567  1_oc1o 8095

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2793  ax-sep 5203  ax-nul 5210  ax-pow 5266

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-v 3496  df-dif 3939  df-un 3941  df-in 3943  df-ss 3952  df-nul 4292  df-pw 4541  df-sn 4568  df-suc 6197  df-1o 8102

This theorem is referenced by:  bnj106  32140  bnj118  32141  bnj121  32142  bnj125  32144  bnj130  32146  bnj153  32152