Theorem bnj105 35221

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 8465	. 2 ⊢ 1o = {∅}
2		p0ex 5353	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2858	1 ⊢ 1o ∈ V

This proof depends on syntax axioms:   ∈ wcel 2145  Vcvv 3453  ∅c0 4282  {csn 4587  1_oc1o 8451

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734  ax-sep 5255  ax-nul 5267  ax-pow 5334

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 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3455  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4283  df-pw 4562  df-sn 4588  df-suc 6367  df-1o 8458

This theorem is used by:  bnj106  35364  bnj118  35365  bnj121  35366  bnj125  35368  bnj130  35370  bnj153  35376