Theorem bnj105 34736

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 8392	. 2 ⊢ 1o = {∅}
2		p0ex 5320	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2827	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2111  Vcvv 3436  ∅c0 4280  {csn 4573  1_oc1o 8378

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 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-sep 5232  ax-nul 5242  ax-pow 5301

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-dif 3900  df-un 3902  df-ss 3914  df-nul 4281  df-pw 4549  df-sn 4574  df-suc 6312  df-1o 8385

This theorem is referenced by:  bnj106  34880  bnj118  34881  bnj121  34882  bnj125  34884  bnj130  34886  bnj153  34892