Theorem bnj105 31996

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 8118	. 2 ⊢ 1o = {∅}
2		p0ex 5287	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2911	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3496  ∅c0 4293  {csn 4569  1_oc1o 8097

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 2795  ax-sep 5205  ax-nul 5212  ax-pow 5268

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 2802  df-cleq 2816  df-clel 2895  df-nfc 2965  df-v 3498  df-dif 3941  df-un 3943  df-in 3945  df-ss 3954  df-nul 4294  df-pw 4543  df-sn 4570  df-suc 6199  df-1o 8104

This theorem is referenced by:  bnj106  32142  bnj118  32143  bnj121  32144  bnj125  32146  bnj130  32148  bnj153  32154