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Mathbox for Rohan Ridenour |
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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 42980 | . 2 ⊢ Scott 𝐴 = {𝑥 ∈ 𝐴 ∣ ∀𝑦 ∈ 𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)} | |
2 | 1 | ssrab3 4079 | 1 ⊢ Scott 𝐴 ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wral 3061 ⊆ wss 3947 ‘cfv 6540 rankcrnk 9754 Scott cscott 42979 |
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 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2703 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-rab 3433 df-v 3476 df-in 3954 df-ss 3964 df-scott 42980 |
This theorem is referenced by: elscottab 42988 |
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