Theorem bnj105 35422

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 8508	. 2 ⊢ 1o = {∅}
2		p0ex 5350	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2860	1 ⊢ 1o ∈ V

This proof depends on syntax axioms:   ∈ wcel 2147  Vcvv 3454  ∅c0 4281  {csn 4588  1_oc1o 8494

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5252  ax-nul 5263  ax-pow 5331

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-dif 4050  df-un 4154  df-nul 4282  df-pw 4562  df-sn 4589  df-suc 6383  df-1o 8501

This theorem is used by:  bnj106  35565  bnj118  35566  bnj121  35567  bnj125  35569  bnj130  35571  bnj153  35577