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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 | β’ β²π₯π΄ |
Ref | Expression |
---|---|
nfscott | β’ β²π₯Scott π΄ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-scott 42608 | . 2 β’ Scott π΄ = {π¦ β π΄ β£ βπ§ β π΄ (rankβπ¦) β (rankβπ§)} | |
2 | nfscott.1 | . . . 4 β’ β²π₯π΄ | |
3 | nfv 1918 | . . . 4 β’ β²π₯(rankβπ¦) β (rankβπ§) | |
4 | 2, 3 | nfralw 3293 | . . 3 β’ β²π₯βπ§ β π΄ (rankβπ¦) β (rankβπ§) |
5 | 4, 2 | nfrabw 3442 | . 2 β’ β²π₯{π¦ β π΄ β£ βπ§ β π΄ (rankβπ¦) β (rankβπ§)} |
6 | 1, 5 | nfcxfr 2902 | 1 β’ β²π₯Scott π΄ |
Colors of variables: wff setvar class |
Syntax hints: β²wnfc 2884 βwral 3061 {crab 3406 β wss 3914 βcfv 6500 rankcrnk 9707 Scott cscott 42607 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ral 3062 df-rab 3407 df-scott 42608 |
This theorem is referenced by: nfcoll 42628 |
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