Theorem bnj95 35561

Description: Technical lemma for bnj124 35568. 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 5401	. 2 ⊢ {⟨∅, pred(𝑥, 𝐴, 𝑅)⟩} ∈ V
3	1, 2	eqeltri 2860	1 ⊢ 𝐹 ∈ V

This proof depends on syntax axioms:   = wceq 1570   ∈ wcel 2147  Vcvv 3454  ∅c0 4281  {csn 4588  ⟨cop 4838   predc-bnj14 35386

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5252  ax-pr 5395

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-un 4154  df-sn 4589  df-pr 4591

This theorem is used by:  bnj124  35568  bnj125  35569  bnj126  35570  bnj150  35573