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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 23197 | . 2 ⊢ toNrmGrp = (𝑔 ∈ V, 𝑓 ∈ V ↦ ((𝑔 sSet 〈(dist‘ndx), (𝑓 ∘ (-g‘𝑔))〉) sSet 〈(TopSet‘ndx), (MetOpen‘(𝑓 ∘ (-g‘𝑔)))〉)) | |
2 | 1 | reldmmpo 7288 | 1 ⊢ Rel dom toNrmGrp |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3497 〈cop 4576 dom cdm 5558 ∘ ccom 5562 Rel wrel 5563 ‘cfv 6358 (class class class)co 7159 ndxcnx 16483 sSet csts 16484 TopSetcts 16574 distcds 16577 -gcsg 18108 MetOpencmopn 20538 toNrmGrp ctng 23191 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2796 ax-sep 5206 ax-nul 5213 ax-pr 5333 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-mo 2621 df-eu 2653 df-clab 2803 df-cleq 2817 df-clel 2896 df-nfc 2966 df-rab 3150 df-v 3499 df-dif 3942 df-un 3944 df-in 3946 df-ss 3955 df-nul 4295 df-if 4471 df-sn 4571 df-pr 4573 df-op 4577 df-br 5070 df-opab 5132 df-xp 5564 df-rel 5565 df-dm 5568 df-oprab 7163 df-mpo 7164 df-tng 23197 |
This theorem is referenced by: tnglem 23252 tngds 23260 tcphval 23824 |
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