Theorem bnj528 35247

Description: Technical lemma for bnj852 35279. 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
bnj528.1	⊢ 𝐺 = (𝑓 ∪ {⟨𝑚, ∪ 𝑦 ∈ (𝑓‘𝑝) pred(𝑦, 𝐴, 𝑅)⟩})

Assertion

Ref	Expression
bnj528	⊢ 𝐺 ∈ V

Proof of Theorem bnj528

Step	Hyp	Ref	Expression
1		bnj528.1	. 2 ⊢ 𝐺 = (𝑓 ∪ {⟨𝑚, ∪ 𝑦 ∈ (𝑓‘𝑝) pred(𝑦, 𝐴, 𝑅)⟩})
2	1	bnj918 35125	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1568   ∈ wcel 2150  Vcvv 3462   ∪ cun 3911  {csn 4594  ⟨cop 4600  ∪ ciun 4961  ‘cfv 6540   predc-bnj14 35047

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2152  ax-9 2160  ax-ext 2742  ax-sep 5262  ax-pr 5408  ax-un 7736

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1571  df-ex 1808  df-sb 2099  df-clab 2749  df-cleq 2762  df-clel 2845  df-v 3464  df-un 3918  df-ss 3930  df-sn 4595  df-pr 4597  df-uni 4878

This theorem is referenced by:  bnj600  35277  bnj908  35289