Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj528 Structured version   Visualization version   GIF version

Theorem bnj528 31501
 Description: Technical lemma for bnj852 31533. 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 ∈ (𝑓𝑝) pred(𝑦, 𝐴, 𝑅)⟩})
Assertion
Ref Expression
bnj528 𝐺 ∈ V

Proof of Theorem bnj528
StepHypRef Expression
1 bnj528.1 . 2 𝐺 = (𝑓 ∪ {⟨𝑚, 𝑦 ∈ (𝑓𝑝) pred(𝑦, 𝐴, 𝑅)⟩})
21bnj918 31378 1 𝐺 ∈ V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1656   ∈ wcel 2164  Vcvv 3414   ∪ cun 3796  {csn 4399  ⟨cop 4405  ∪ ciun 4742  ‘cfv 6127   predc-bnj14 31299 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-8 2166  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803  ax-sep 5007  ax-nul 5015  ax-pr 5129  ax-un 7214 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-rex 3123  df-v 3416  df-dif 3801  df-un 3803  df-nul 4147  df-sn 4400  df-pr 4402  df-uni 4661 This theorem is referenced by:  bnj600  31531  bnj908  31543
 Copyright terms: Public domain W3C validator