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 40662 | . 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 3225 | . . 3 ⊢ Ⅎ𝑥∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧) |
5 | 4, 2 | nfrabw 3385 | . 2 ⊢ Ⅎ𝑥{𝑦 ∈ 𝐴 ∣ ∀𝑧 ∈ 𝐴 (rank‘𝑦) ⊆ (rank‘𝑧)} |
6 | 1, 5 | nfcxfr 2975 | 1 ⊢ Ⅎ𝑥Scott 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2961 ∀wral 3138 {crab 3142 ⊆ wss 3924 ‘cfv 6341 rankcrnk 9178 Scott cscott 40661 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rab 3147 df-scott 40662 |
This theorem is referenced by: nfcoll 40682 |
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