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Theorem nfscott 44263
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 44260 . 2 Scott 𝐴 = {𝑦𝐴 ∣ ∀𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)}
2 nfscott.1 . . . 4 𝑥𝐴
3 nfv 1913 . . . 4 𝑥(rank‘𝑦) ⊆ (rank‘𝑧)
42, 3nfralw 3310 . . 3 𝑥𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)
54, 2nfrabw 3474 . 2 𝑥{𝑦𝐴 ∣ ∀𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)}
61, 5nfcxfr 2902 1 𝑥Scott 𝐴
Colors of variables: wff setvar class
Syntax hints:  wnfc 2889  wral 3060  {crab 3435  wss 3950  cfv 6560  rankcrnk 9804  Scott cscott 44259
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-10 2140  ax-11 2156  ax-12 2176  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-nf 1783  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-nfc 2891  df-ral 3061  df-rab 3436  df-scott 44260
This theorem is referenced by:  nfcoll  44280
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