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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 | ⊢ Rel dom toNrmGrp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-tng 22389 | . 2 ⊢ toNrmGrp = (𝑔 ∈ V, 𝑓 ∈ V ↦ ((𝑔 sSet 〈(dist‘ndx), (𝑓 ∘ (-g‘𝑔))〉) sSet 〈(TopSet‘ndx), (MetOpen‘(𝑓 ∘ (-g‘𝑔)))〉)) | |
2 | 1 | reldmmpt2 6771 | 1 ⊢ Rel dom toNrmGrp |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3200 〈cop 4183 dom cdm 5114 ∘ ccom 5118 Rel wrel 5119 ‘cfv 5888 (class class class)co 6650 ndxcnx 15854 sSet csts 15855 TopSetcts 15947 distcds 15950 -gcsg 17424 MetOpencmopn 19736 toNrmGrp ctng 22383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-dm 5124 df-oprab 6654 df-mpt2 6655 df-tng 22389 |
This theorem is referenced by: tnglem 22444 tngds 22452 tchval 23017 |
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