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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 16148. (Contributed by NM, 20-Oct-2012.) |
Ref | Expression |
---|---|
plusgid | ⊢ +g = Slot (+g‘ndx) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-plusg 16148 | . 2 ⊢ +g = Slot 2 | |
2 | 2nn 11369 | . 2 ⊢ 2 ∈ ℕ | |
3 | 1, 2 | ndxid 16077 | 1 ⊢ +g = Slot (+g‘ndx) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1624 ‘cfv 6041 2c2 11254 ndxcnx 16048 Slot cslot 16050 +gcplusg 16135 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1863 ax-4 1878 ax-5 1980 ax-6 2046 ax-7 2082 ax-8 2133 ax-9 2140 ax-10 2160 ax-11 2175 ax-12 2188 ax-13 2383 ax-ext 2732 ax-sep 4925 ax-nul 4933 ax-pow 4984 ax-pr 5047 ax-un 7106 ax-cnex 10176 ax-resscn 10177 ax-1cn 10178 ax-icn 10179 ax-addcl 10180 ax-addrcl 10181 ax-mulcl 10182 ax-mulrcl 10183 ax-i2m1 10188 ax-1ne0 10189 ax-rrecex 10192 ax-cnre 10193 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3or 1073 df-3an 1074 df-tru 1627 df-ex 1846 df-nf 1851 df-sb 2039 df-eu 2603 df-mo 2604 df-clab 2739 df-cleq 2745 df-clel 2748 df-nfc 2883 df-ne 2925 df-ral 3047 df-rex 3048 df-reu 3049 df-rab 3051 df-v 3334 df-sbc 3569 df-csb 3667 df-dif 3710 df-un 3712 df-in 3714 df-ss 3721 df-pss 3723 df-nul 4051 df-if 4223 df-pw 4296 df-sn 4314 df-pr 4316 df-tp 4318 df-op 4320 df-uni 4581 df-iun 4666 df-br 4797 df-opab 4857 df-mpt 4874 df-tr 4897 df-id 5166 df-eprel 5171 df-po 5179 df-so 5180 df-fr 5217 df-we 5219 df-xp 5264 df-rel 5265 df-cnv 5266 df-co 5267 df-dm 5268 df-rn 5269 df-res 5270 df-ima 5271 df-pred 5833 df-ord 5879 df-on 5880 df-lim 5881 df-suc 5882 df-iota 6004 df-fun 6043 df-fn 6044 df-f 6045 df-f1 6046 df-fo 6047 df-f1o 6048 df-fv 6049 df-ov 6808 df-om 7223 df-wrecs 7568 df-recs 7629 df-rdg 7667 df-nn 11205 df-2 11263 df-ndx 16054 df-slot 16055 df-plusg 16148 |
This theorem is referenced by: rngplusg 16196 srngplusg 16204 lmodplusg 16213 ipsaddg 16220 phlplusg 16230 topgrpplusg 16238 odrngplusg 16262 prdsplusg 16312 imasplusg 16371 grpss 17633 oppgplusfval 17970 symgplusg 18001 mgpplusg 18685 rmodislmod 19125 psrplusg 19575 cnfldadd 19945 matplusg 20414 algaddg 38243 cznabel 42456 cznrng 42457 |
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