![]() |
Mathbox for Richard Penner |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > ntrf2 | Structured version Visualization version GIF version |
Description: The interior function is a map from the powerset of the base set to itself. (Contributed by RP, 22-Apr-2021.) |
Ref | Expression |
---|---|
ntrrn.x | β’ π = βͺ π½ |
ntrrn.i | β’ πΌ = (intβπ½) |
Ref | Expression |
---|---|
ntrf2 | β’ (π½ β Top β πΌ:π« πβΆπ« π) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ntrrn.x | . . 3 β’ π = βͺ π½ | |
2 | ntrrn.i | . . 3 β’ πΌ = (intβπ½) | |
3 | 1, 2 | ntrf 43547 | . 2 β’ (π½ β Top β πΌ:π« πβΆπ½) |
4 | 1 | toptopon 22812 | . . . 4 β’ (π½ β Top β π½ β (TopOnβπ)) |
5 | topgele 22825 | . . . 4 β’ (π½ β (TopOnβπ) β ({β , π} β π½ β§ π½ β π« π)) | |
6 | 4, 5 | sylbi 216 | . . 3 β’ (π½ β Top β ({β , π} β π½ β§ π½ β π« π)) |
7 | 6 | simprd 495 | . 2 β’ (π½ β Top β π½ β π« π) |
8 | 3, 7 | fssd 6734 | 1 β’ (π½ β Top β πΌ:π« πβΆπ« π) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β§ wa 395 = wceq 1534 β wcel 2099 β wss 3945 β c0 4318 π« cpw 4598 {cpr 4626 βͺ cuni 4903 βΆwf 6538 βcfv 6542 Topctop 22788 TopOnctopon 22805 intcnt 22914 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2699 ax-rep 5279 ax-sep 5293 ax-nul 5300 ax-pow 5359 ax-pr 5423 ax-un 7734 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2530 df-eu 2559 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2937 df-ral 3058 df-rex 3067 df-reu 3373 df-rab 3429 df-v 3472 df-sbc 3776 df-csb 3891 df-dif 3948 df-un 3950 df-in 3952 df-ss 3962 df-nul 4319 df-if 4525 df-pw 4600 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-iun 4993 df-br 5143 df-opab 5205 df-mpt 5226 df-id 5570 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-rn 5683 df-res 5684 df-ima 5685 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-top 22789 df-topon 22806 df-ntr 22917 |
This theorem is referenced by: ntrelmap 43549 |
Copyright terms: Public domain | W3C validator |