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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 23963 | . 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 7494 | 1 β’ Rel dom toNrmGrp |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3447 β¨cop 4596 dom cdm 5637 β ccom 5641 Rel wrel 5642 βcfv 6500 (class class class)co 7361 sSet csts 17043 ndxcnx 17073 TopSetcts 17147 distcds 17150 -gcsg 18758 MetOpencmopn 20809 toNrmGrp ctng 23957 |
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 ax-sep 5260 ax-nul 5267 ax-pr 5388 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-rab 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-br 5110 df-opab 5172 df-xp 5643 df-rel 5644 df-dm 5647 df-oprab 7365 df-mpo 7366 df-tng 23963 |
This theorem is referenced by: tnglem 24019 tnglemOLD 24020 tngds 24034 tngdsOLD 24035 tcphval 24605 |
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