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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 24730 | . 2 ⊢ NGHom = (𝑠 ∈ NrmGrp, 𝑡 ∈ NrmGrp ↦ (◡(𝑠 normOp 𝑡) “ ℝ)) | |
| 2 | 1 | reldmmpo 7567 | 1 ⊢ Rel dom NGHom |
| Colors of variables: wff setvar class |
| Syntax hints: ◡ccnv 5684 dom cdm 5685 “ cima 5688 Rel wrel 5690 (class class class)co 7431 ℝcr 11154 NrmGrpcngp 24590 normOp cnmo 24726 NGHom cnghm 24727 |
| 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 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pr 5432 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2540 df-eu 2569 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-br 5144 df-opab 5206 df-xp 5691 df-rel 5692 df-dm 5695 df-oprab 7435 df-mpo 7436 df-nghm 24730 |
| This theorem is referenced by: (None) |
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