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| Description: The class of all complex Hilbert spaces is a relation. (Contributed by NM, 17-Mar-2007.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| hlrel | ⊢ Rel CHilOLD | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | hlobn 30907 | . . 3 ⊢ (𝑥 ∈ CHilOLD → 𝑥 ∈ CBan) | |
| 2 | 1 | ssriv 3987 | . 2 ⊢ CHilOLD ⊆ CBan | 
| 3 | bnrel 30886 | . 2 ⊢ Rel CBan | |
| 4 | relss 5791 | . 2 ⊢ (CHilOLD ⊆ CBan → (Rel CBan → Rel CHilOLD)) | |
| 5 | 2, 3, 4 | mp2 9 | 1 ⊢ Rel CHilOLD | 
| Colors of variables: wff setvar class | 
| Syntax hints: ⊆ wss 3951 Rel wrel 5690 CBanccbn 30881 CHilOLDchlo 30904 | 
| 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-11 2157 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-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-in 3958 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-opab 5206 df-xp 5691 df-rel 5692 df-iota 6514 df-fv 6569 df-oprab 7435 df-nv 30611 df-cbn 30882 df-hlo 30905 | 
| This theorem is referenced by: (None) | 
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