Theorem bnj105 32703

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 8304	. 2 ⊢ 1o = {∅}
2		p0ex 5307	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2835	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2106  Vcvv 3432  ∅c0 4256  {csn 4561  1_oc1o 8290

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709  ax-sep 5223  ax-nul 5230  ax-pow 5288

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-pw 4535  df-sn 4562  df-suc 6272  df-1o 8297

This theorem is referenced by:  bnj106  32848  bnj118  32849  bnj121  32850  bnj125  32852  bnj130  32854  bnj153  32860