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| Mirrors > Home > MPE Home > Th. List > reldmsets | Structured version Visualization version GIF version | ||
| Description: The structure override operator is a proper operator. (Contributed by Stefan O'Rear, 29-Jan-2015.) |
| Ref | Expression |
|---|---|
| reldmsets | ⊢ Rel dom sSet |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-sets 17201 | . 2 ⊢ sSet = (𝑠 ∈ V, 𝑒 ∈ V ↦ ((𝑠 ↾ (V ∖ dom {𝑒})) ∪ {𝑒})) | |
| 2 | 1 | reldmmpo 7567 | 1 ⊢ Rel dom sSet |
| Colors of variables: wff setvar class |
| Syntax hints: Vcvv 3480 ∖ cdif 3948 ∪ cun 3949 {csn 4626 dom cdm 5685 ↾ cres 5687 Rel wrel 5690 sSet csts 17200 |
| 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-sets 17201 |
| This theorem is referenced by: setsnid 17245 setsnidOLD 17246 oduval 18333 oduleval 18334 oppgval 19365 oppgplusfval 19366 mgpval 20140 opprval 20335 |
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