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Mirrors > Home > MPE Home > Th. List > reldmtng | Structured version Visualization version GIF version |
Description: The function toNrmGrp is a two-argument function. (Contributed by Mario Carneiro, 8-Oct-2015.) |
Ref | Expression |
---|---|
reldmtng | β’ Rel dom toNrmGrp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-tng 24314 | . 2 β’ toNrmGrp = (π β V, π β V β¦ ((π sSet β¨(distβndx), (π β (-gβπ))β©) sSet β¨(TopSetβndx), (MetOpenβ(π β (-gβπ)))β©)) | |
2 | 1 | reldmmpo 7546 | 1 β’ Rel dom toNrmGrp |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3473 β¨cop 4635 dom cdm 5677 β ccom 5681 Rel wrel 5682 βcfv 6544 (class class class)co 7412 sSet csts 17101 ndxcnx 17131 TopSetcts 17208 distcds 17211 -gcsg 18858 MetOpencmopn 21135 toNrmGrp ctng 24308 |
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 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-sep 5300 ax-nul 5307 ax-pr 5428 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-rab 3432 df-v 3475 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-br 5150 df-opab 5212 df-xp 5683 df-rel 5684 df-dm 5687 df-oprab 7416 df-mpo 7417 df-tng 24314 |
This theorem is referenced by: tnglem 24370 tnglemOLD 24371 tngds 24385 tngdsOLD 24386 tcphval 24967 |
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