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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 24100 | . 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 7545 | 1 β’ Rel dom toNrmGrp |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3474 β¨cop 4634 dom cdm 5676 β ccom 5680 Rel wrel 5681 βcfv 6543 (class class class)co 7411 sSet csts 17098 ndxcnx 17128 TopSetcts 17205 distcds 17208 -gcsg 18823 MetOpencmopn 20940 toNrmGrp ctng 24094 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5299 ax-nul 5306 ax-pr 5427 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-rab 3433 df-v 3476 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-sn 4629 df-pr 4631 df-op 4635 df-br 5149 df-opab 5211 df-xp 5682 df-rel 5683 df-dm 5686 df-oprab 7415 df-mpo 7416 df-tng 24100 |
This theorem is referenced by: tnglem 24156 tnglemOLD 24157 tngds 24171 tngdsOLD 24172 tcphval 24742 |
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