Theorem bnj105 34738

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 8513	. 2 ⊢ 1o = {∅}
2		p0ex 5384	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2837	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2108  Vcvv 3480  ∅c0 4333  {csn 4626  1_oc1o 8499

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pow 5365

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-pw 4602  df-sn 4627  df-suc 6390  df-1o 8506

This theorem is referenced by:  bnj106  34882  bnj118  34883  bnj121  34884  bnj125  34886  bnj130  34888  bnj153  34894