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Theorem nfscott 44235
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 44232 . 2 Scott 𝐴 = {𝑦𝐴 ∣ ∀𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)}
2 nfscott.1 . . . 4 𝑥𝐴
3 nfv 1912 . . . 4 𝑥(rank‘𝑦) ⊆ (rank‘𝑧)
42, 3nfralw 3309 . . 3 𝑥𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)
54, 2nfrabw 3473 . 2 𝑥{𝑦𝐴 ∣ ∀𝑧𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)}
61, 5nfcxfr 2901 1 𝑥Scott 𝐴
Colors of variables: wff setvar class
Syntax hints:  wnfc 2888  wral 3059  {crab 3433  wss 3963  cfv 6563  rankcrnk 9801  Scott cscott 44231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ral 3060  df-rab 3434  df-scott 44232
This theorem is referenced by:  nfcoll  44252
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