Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 16484 | . 2 ⊢ sSet = (𝑠 ∈ V, 𝑒 ∈ V ↦ ((𝑠 ↾ (V ∖ dom {𝑒})) ∪ {𝑒})) | |
2 | 1 | reldmmpo 7279 | 1 ⊢ Rel dom sSet |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3495 ∖ cdif 3933 ∪ cun 3934 {csn 4561 dom cdm 5550 ↾ cres 5552 Rel wrel 5555 sSet csts 16475 |
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 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2156 ax-12 2172 ax-ext 2793 ax-sep 5196 ax-nul 5203 ax-pr 5322 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-mo 2618 df-eu 2650 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-v 3497 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-nul 4292 df-if 4468 df-sn 4562 df-pr 4564 df-op 4568 df-br 5060 df-opab 5122 df-xp 5556 df-rel 5557 df-dm 5560 df-oprab 7154 df-mpo 7155 df-sets 16484 |
This theorem is referenced by: setsnid 16533 oduval 17734 oduleval 17735 oppgval 18469 oppgplusfval 18470 mgpval 19236 opprval 19368 |
Copyright terms: Public domain | W3C validator |