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 40646 | . 2 ⊢ Scott 𝐴 = {𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} | |
2 | nfscott.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | nfv 1914 | . . . 4 ⊢ Ⅎ𝑥(rank‘𝑦) ⊆ (rank‘𝑧) | |
4 | 2, 3 | nfralw 3224 | . . 3 ⊢ Ⅎ𝑥∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧) |
5 | 4, 2 | nfrabw 3384 | . 2 ⊢ Ⅎ𝑥{𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} |
6 | 1, 5 | nfcxfr 2974 | 1 ⊢ Ⅎ𝑥Scott 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2960 ∀wral 3137 {crab 3141 ⊆ wss 3929 ‘cfv 6348 rankcrnk 9185 Scott cscott 40645 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2792 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2799 df-cleq 2813 df-clel 2892 df-nfc 2962 df-ral 3142 df-rab 3146 df-scott 40646 |
This theorem is referenced by: nfcoll 40666 |
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