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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 24093 | . 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 7543 | 1 β’ Rel dom toNrmGrp |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3475 β¨cop 4635 dom cdm 5677 β ccom 5681 Rel wrel 5682 βcfv 6544 (class class class)co 7409 sSet csts 17096 ndxcnx 17126 TopSetcts 17203 distcds 17206 -gcsg 18821 MetOpencmopn 20934 toNrmGrp ctng 24087 |
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 5300 ax-nul 5307 ax-pr 5428 |
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 3434 df-v 3477 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 7413 df-mpo 7414 df-tng 24093 |
This theorem is referenced by: tnglem 24149 tnglemOLD 24150 tngds 24164 tngdsOLD 24165 tcphval 24735 |
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