Mathbox for Rohan Ridenour < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nfscott Structured version   Visualization version   GIF version

Theorem nfscott 40871
 Description: Bound-variable hypothesis builder for the Scott operation. (Contributed by Rohan Ridenour, 11-Aug-2023.)
Hypothesis
Ref Expression
nfscott.1 𝑥𝐴
Assertion
Ref Expression
nfscott 𝑥Scott 𝐴

Proof of Theorem nfscott
Dummy variables 𝑦 𝑧 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-scott 40868 . 2 Scott 𝐴 = {𝑦𝐴 ∣ ∀𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)}
2 nfscott.1 . . . 4 𝑥𝐴
3 nfv 1916 . . . 4 𝑥(rank‘𝑦) ⊆ (rank‘𝑧)
42, 3nfralw 3219 . . 3 𝑥𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)
54, 2nfrabw 3376 . 2 𝑥{𝑦𝐴 ∣ ∀𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)}
61, 5nfcxfr 2980 1 𝑥Scott 𝐴
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2962  ∀wral 3133  {crab 3137   ⊆ wss 3919  ‘cfv 6343  rankcrnk 9189  Scott cscott 40867 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rab 3142  df-scott 40868 This theorem is referenced by:  nfcoll  40888
 Copyright terms: Public domain W3C validator