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Mathbox for Rohan Ridenour |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfscott | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for the Scott operation. (Contributed by Rohan Ridenour, 11-Aug-2023.) |
Ref | Expression |
---|---|
nfscott.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfscott | ⊢ Ⅎ𝑥Scott 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-scott 44232 | . 2 ⊢ Scott 𝐴 = {𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} | |
2 | nfscott.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | nfv 1912 | . . . 4 ⊢ Ⅎ𝑥(rank‘𝑦) ⊆ (rank‘𝑧) | |
4 | 2, 3 | nfralw 3309 | . . 3 ⊢ Ⅎ𝑥∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧) |
5 | 4, 2 | nfrabw 3473 | . 2 ⊢ Ⅎ𝑥{𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} |
6 | 1, 5 | nfcxfr 2901 | 1 ⊢ Ⅎ𝑥Scott 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 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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