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| Mirrors > Home > MPE Home > Th. List > Mathboxes > scottss | Structured version Visualization version GIF version | ||
| Description: Scott's trick produces a subset of the input class. (Contributed by Rohan Ridenour, 11-Aug-2023.) | 
| Ref | Expression | 
|---|---|
| scottss | ⊢ Scott 𝐴 ⊆ 𝐴 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-scott 44260 | . 2 ⊢ Scott 𝐴 = {𝑥 ∈ 𝐴 ∣ ∀𝑦 ∈ 𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)} | |
| 2 | 1 | ssrab3 4081 | 1 ⊢ Scott 𝐴 ⊆ 𝐴 | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∀wral 3060 ⊆ 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-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-rab 3436 df-ss 3967 df-scott 44260 | 
| This theorem is referenced by: elscottab 44268 | 
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