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Mirrors > Home > MPE Home > Th. List > reldmress | Structured version Visualization version GIF version |
Description: The structure restriction is a proper operator, so it can be used with ovprc1 7397. (Contributed by Stefan O'Rear, 29-Nov-2014.) |
Ref | Expression |
---|---|
reldmress | β’ Rel dom βΎs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ress 17118 | . 2 β’ βΎs = (π€ β V, π β V β¦ if((Baseβπ€) β π, π€, (π€ sSet β¨(Baseβndx), (π β© (Baseβπ€))β©))) | |
2 | 1 | reldmmpo 7491 | 1 β’ Rel dom βΎs |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3444 β© cin 3910 β wss 3911 ifcif 4487 β¨cop 4593 dom cdm 5634 Rel wrel 5639 βcfv 6497 (class class class)co 7358 sSet csts 17040 ndxcnx 17070 Basecbs 17088 βΎs cress 17117 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5257 ax-nul 5264 ax-pr 5385 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-rab 3407 df-v 3446 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-nul 4284 df-if 4488 df-sn 4588 df-pr 4590 df-op 4594 df-br 5107 df-opab 5169 df-xp 5640 df-rel 5641 df-dm 5644 df-oprab 7362 df-mpo 7363 df-ress 17118 |
This theorem is referenced by: ressbas 17123 ressbasOLD 17124 ressbasss 17126 resseqnbas 17127 resslemOLD 17128 ress0 17129 ressinbas 17131 ressress 17134 wunress 17136 wunressOLD 17137 subcmn 19620 srasca 20662 srascaOLD 20663 rlmsca2 20686 resstopn 22553 cphsubrglem 24557 submomnd 31967 suborng 32157 ressbasssg 40714 |
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