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Mirrors > Home > MPE Home > Th. List > reldmnghm | Structured version Visualization version GIF version |
Description: Lemma for normed group homomorphisms. (Contributed by Mario Carneiro, 18-Oct-2015.) |
Ref | Expression |
---|---|
reldmnghm | ⊢ Rel dom NGHom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nghm 24670 | . 2 ⊢ NGHom = (𝑠 ∈ NrmGrp, 𝑡 ∈ NrmGrp ↦ (◡(𝑠 normOp 𝑡) “ ℝ)) | |
2 | 1 | reldmmpo 7555 | 1 ⊢ Rel dom NGHom |
Colors of variables: wff setvar class |
Syntax hints: ◡ccnv 5677 dom cdm 5678 “ cima 5681 Rel wrel 5683 (class class class)co 7419 ℝcr 11139 NrmGrpcngp 24530 normOp cnmo 24666 NGHom cnghm 24667 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5300 ax-nul 5307 ax-pr 5429 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-rab 3419 df-v 3463 df-dif 3947 df-un 3949 df-ss 3961 df-nul 4323 df-if 4531 df-sn 4631 df-pr 4633 df-op 4637 df-br 5150 df-opab 5212 df-xp 5684 df-rel 5685 df-dm 5688 df-oprab 7423 df-mpo 7424 df-nghm 24670 |
This theorem is referenced by: (None) |
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