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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 17198 | . 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 3478 ∖ cdif 3960 ∪ cun 3961 {csn 4631 dom cdm 5689 ↾ cres 5691 Rel wrel 5694 sSet csts 17197 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-ext 2706 ax-sep 5302 ax-nul 5312 ax-pr 5438 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-nf 1781 df-sb 2063 df-mo 2538 df-eu 2567 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-rab 3434 df-v 3480 df-dif 3966 df-un 3968 df-ss 3980 df-nul 4340 df-if 4532 df-sn 4632 df-pr 4634 df-op 4638 df-br 5149 df-opab 5211 df-xp 5695 df-rel 5696 df-dm 5699 df-oprab 7435 df-mpo 7436 df-sets 17198 |
This theorem is referenced by: setsnid 17243 setsnidOLD 17244 oduval 18345 oduleval 18346 oppgval 19378 oppgplusfval 19379 mgpval 20155 opprval 20352 |
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