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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 40944 | . 2 ⊢ Scott 𝐴 = {𝑥 ∈ 𝐴 ∣ ∀𝑦 ∈ 𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)} | |
2 | 1 | ssrab3 4008 | 1 ⊢ Scott 𝐴 ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wral 3106 ⊆ wss 3881 ‘cfv 6324 rankcrnk 9176 Scott cscott 40943 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1541 df-ex 1782 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-rab 3115 df-v 3443 df-in 3888 df-ss 3898 df-scott 40944 |
This theorem is referenced by: elscottab 40952 |
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