Theorem bnj95 35161

Description: Technical lemma for bnj124 35168. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj95.1	⊢ 𝐹 = {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩}

Assertion

Ref	Expression
bnj95	⊢ 𝐹 ∈ V

Proof of Theorem bnj95

Step	Hyp	Ref	Expression
1		bnj95.1	. 2 ⊢ 𝐹 = {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩}
2		snex 5398	. 2 ⊢ {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩} ∈ V
3	1, 2	eqeltri 2860	1 ⊢ 𝐹 ∈ V

Syntax hints:   = wceq 1562   ∈ wcel 2144  Vcvv 3456  ∅c0 4287  {csn 4584  ⟨cop 4590   predc-bnj14 34986

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-ext 2736  ax-sep 5248  ax-pr 5392

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1565  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-v 3458  df-un 3911  df-sn 4585  df-pr 4587

This theorem is referenced by:  bnj124  35168  bnj125  35169  bnj126  35170  bnj150  35173