Theorem bnj95 32744

Description: Technical lemma for bnj124 32751. 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 5349	. 2 ⊢ {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩} ∈ V
3	1, 2	eqeltri 2835	1 ⊢ 𝐹 ∈ V

Syntax hints:   = wceq 1539   ∈ wcel 2108  Vcvv 3422  ∅c0 4253  {csn 4558  ⟨cop 4564   predc-bnj14 32567

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-sep 5218  ax-nul 5225  ax-pr 5347

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-dif 3886  df-un 3888  df-nul 4254  df-sn 4559  df-pr 4561

This theorem is referenced by:  bnj124  32751  bnj125  32752  bnj126  32753  bnj150  32756