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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 44260 | . 2 ⊢ Scott 𝐴 = {𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} | |
| 2 | nfscott.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
| 3 | nfv 1913 | . . . 4 ⊢ Ⅎ𝑥(rank‘𝑦) ⊆ (rank‘𝑧) | |
| 4 | 2, 3 | nfralw 3310 | . . 3 ⊢ Ⅎ𝑥∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧) | 
| 5 | 4, 2 | nfrabw 3474 | . 2 ⊢ Ⅎ𝑥{𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} | 
| 6 | 1, 5 | nfcxfr 2902 | 1 ⊢ Ⅎ𝑥Scott 𝐴 | 
| Colors of variables: wff setvar class | 
| Syntax hints: Ⅎwnfc 2889 ∀wral 3060 {crab 3435 ⊆ 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-10 2140 ax-11 2156 ax-12 2176 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1542 df-ex 1779 df-nf 1783 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-nfc 2891 df-ral 3061 df-rab 3436 df-scott 44260 | 
| This theorem is referenced by: nfcoll 44280 | 
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