Theorem bnj105 34700

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 8529	. 2 ⊢ 1o = {∅}
2		p0ex 5402	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2840	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2108  Vcvv 3488  ∅c0 4352  {csn 4648  1_oc1o 8515

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-sep 5317  ax-nul 5324  ax-pow 5383

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-pw 4624  df-sn 4649  df-suc 6401  df-1o 8522

This theorem is referenced by:  bnj106  34844  bnj118  34845  bnj121  34846  bnj125  34848  bnj130  34850  bnj153  34856