Theorem bnj528 33900

Description: Technical lemma for bnj852 33932. 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 33777	1 ⊢ 𝐺 ∈ V

Syntax hints:   = wceq 1542   ∈ wcel 2107  Vcvv 3475   ∪ cun 3947  {csn 4629  ⟨cop 4635  ∪ ciun 4998  ‘cfv 6544   predc-bnj14 33699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5300  ax-nul 5307  ax-pr 5428  ax-un 7725

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-sn 4630  df-pr 4632  df-uni 4910

This theorem is referenced by:  bnj600  33930  bnj908  33942