Theorem bnj105 34701

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 8485	. 2 ⊢ 1o = {∅}
2		p0ex 5354	. 2 ⊢ {∅} ∈ V
3	1, 2	eqeltri 2830	1 ⊢ 1o ∈ V

Syntax hints:   ∈ wcel 2108  Vcvv 3459  ∅c0 4308  {csn 4601  1_oc1o 8471

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 2707  ax-sep 5266  ax-nul 5276  ax-pow 5335

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-v 3461  df-dif 3929  df-un 3931  df-ss 3943  df-nul 4309  df-pw 4577  df-sn 4602  df-suc 6358  df-1o 8478

This theorem is referenced by:  bnj106  34845  bnj118  34846  bnj121  34847  bnj125  34849  bnj130  34851  bnj153  34857