Theorem bnj95 35061

Description: Technical lemma for bnj124 35068. 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 5371	. 2 ⊢ {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩} ∈ V
3	1, 2	eqeltri 2837	1 ⊢ 𝐹 ∈ V

Syntax hints:   = wceq 1548   ∈ wcel 2121  Vcvv 3433  ∅c0 4264  {csn 4558  ⟨cop 4564   predc-bnj14 34886

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-ext 2713  ax-sep 5221  ax-pr 5365

This theorem depends on definitions:  df-bi 209  df-an 398  df-or 855  df-tru 1551  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-v 3435  df-un 3890  df-sn 4559  df-pr 4561

This theorem is referenced by:  bnj124  35068  bnj125  35069  bnj126  35070  bnj150  35073