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| Mirrors > Home > MPE Home > Th. List > plusgid | Structured version Visualization version GIF version | ||
| Description: Utility theorem: index-independent form of df-plusg 17310. (Contributed by NM, 20-Oct-2012.) |
| Ref | Expression |
|---|---|
| plusgid | ⊢ +g = Slot (+g‘ndx) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-plusg 17310 | . 2 ⊢ +g = Slot 2 | |
| 2 | 2nn 12339 | . 2 ⊢ 2 ∈ ℕ | |
| 3 | 1, 2 | ndxid 17234 | 1 ⊢ +g = Slot (+g‘ndx) |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ‘cfv 6561 2c2 12321 Slot cslot 17218 ndxcnx 17230 +gcplusg 17297 |
| 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-pow 5365 ax-pr 5432 ax-un 7755 ax-cnex 11211 ax-1cn 11213 ax-addcl 11215 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3or 1088 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-ne 2941 df-ral 3062 df-rex 3071 df-reu 3381 df-rab 3437 df-v 3482 df-sbc 3789 df-csb 3900 df-dif 3954 df-un 3956 df-in 3958 df-ss 3968 df-pss 3971 df-nul 4334 df-if 4526 df-pw 4602 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-iun 4993 df-br 5144 df-opab 5206 df-mpt 5226 df-tr 5260 df-id 5578 df-eprel 5584 df-po 5592 df-so 5593 df-fr 5637 df-we 5639 df-xp 5691 df-rel 5692 df-cnv 5693 df-co 5694 df-dm 5695 df-rn 5696 df-res 5697 df-ima 5698 df-pred 6321 df-ord 6387 df-on 6388 df-lim 6389 df-suc 6390 df-iota 6514 df-fun 6563 df-fn 6564 df-f 6565 df-f1 6566 df-fo 6567 df-f1o 6568 df-fv 6569 df-ov 7434 df-om 7888 df-2nd 8015 df-frecs 8306 df-wrecs 8337 df-recs 8411 df-rdg 8450 df-nn 12267 df-2 12329 df-slot 17219 df-ndx 17231 df-plusg 17310 |
| This theorem is referenced by: grpplusg 17332 ressplusg 17334 rngplusg 17344 srngplusg 17355 lmodplusg 17371 ipsaddg 17382 phlplusg 17392 topgrpplusg 17407 odrngplusg 17449 prdsplusg 17503 imasplusg 17562 frmdplusg 18867 efmndplusg 18893 grpss 18972 oppgplusfval 19366 mgpplusg 20141 oppradd 20343 rmodislmod 20928 sraaddg 21179 mpocnfldadd 21369 cnfldaddOLD 21384 zlmplusg 21531 znadd 21557 psrplusg 21956 opsrplusg 22071 ply1plusgfvi 22243 matplusg 22418 tngplusg 24657 ttgplusg 28889 rlocaddval 33272 resvplusg 33361 idlsrgplusg 33533 bj-endcomp 37318 hlhilsplus 41944 opprmndb 42521 opprgrpb 42522 opprablb 42523 algaddg 43187 mendplusgfval 43193 mnringaddgd 44236 cznabel 48176 cznrng 48177 |
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