Theorem bnj95 34393

Description: Technical lemma for bnj124 34400. 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 5422	. 2 ⊢ {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩} ∈ V
3	1, 2	eqeltri 2821	1 ⊢ 𝐹 ∈ V

Syntax hints:   = wceq 1533   ∈ wcel 2098  Vcvv 3466  ∅c0 4315  {csn 4621  ⟨cop 4627   predc-bnj14 34217

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-dif 3944  df-un 3946  df-nul 4316  df-sn 4622  df-pr 4624

This theorem is referenced by:  bnj124  34400  bnj125  34401  bnj126  34402  bnj150  34405