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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 40944 | . 2 ⊢ Scott 𝐴 = {𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} | |
2 | nfscott.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | nfv 1915 | . . . 4 ⊢ Ⅎ𝑥(rank‘𝑦) ⊆ (rank‘𝑧) | |
4 | 2, 3 | nfralw 3189 | . . 3 ⊢ Ⅎ𝑥∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧) |
5 | 4, 2 | nfrabw 3338 | . 2 ⊢ Ⅎ𝑥{𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} |
6 | 1, 5 | nfcxfr 2953 | 1 ⊢ Ⅎ𝑥Scott 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2936 ∀wral 3106 {crab 3110 ⊆ 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-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ral 3111 df-rab 3115 df-scott 40944 |
This theorem is referenced by: nfcoll 40964 |
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