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Mirrors > Home > MPE Home > Th. List > ipndx | Structured version Visualization version GIF version |
Description: Index value of the df-ip 17151 slot. (Contributed by Mario Carneiro, 14-Aug-2015.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ipndx | ⊢ (·𝑖‘ndx) = 8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ip 17151 | . 2 ⊢ ·𝑖 = Slot 8 | |
2 | 8nn 12248 | . 2 ⊢ 8 ∈ ℕ | |
3 | 1, 2 | ndxarg 17068 | 1 ⊢ (·𝑖‘ndx) = 8 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 ‘cfv 6496 8c8 12214 ndxcnx 17065 ·𝑖cip 17138 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2707 ax-sep 5256 ax-nul 5263 ax-pow 5320 ax-pr 5384 ax-un 7672 ax-cnex 11107 ax-1cn 11109 ax-addcl 11111 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2538 df-eu 2567 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2889 df-ne 2944 df-ral 3065 df-rex 3074 df-reu 3354 df-rab 3408 df-v 3447 df-sbc 3740 df-csb 3856 df-dif 3913 df-un 3915 df-in 3917 df-ss 3927 df-pss 3929 df-nul 4283 df-if 4487 df-pw 4562 df-sn 4587 df-pr 4589 df-op 4593 df-uni 4866 df-iun 4956 df-br 5106 df-opab 5168 df-mpt 5189 df-tr 5223 df-id 5531 df-eprel 5537 df-po 5545 df-so 5546 df-fr 5588 df-we 5590 df-xp 5639 df-rel 5640 df-cnv 5641 df-co 5642 df-dm 5643 df-rn 5644 df-res 5645 df-ima 5646 df-pred 6253 df-ord 6320 df-on 6321 df-lim 6322 df-suc 6323 df-iota 6448 df-fun 6498 df-fn 6499 df-f 6500 df-f1 6501 df-fo 6502 df-f1o 6503 df-fv 6504 df-ov 7360 df-om 7803 df-2nd 7922 df-frecs 8212 df-wrecs 8243 df-recs 8317 df-rdg 8356 df-nn 12154 df-2 12216 df-3 12217 df-4 12218 df-5 12219 df-6 12220 df-7 12221 df-8 12222 df-slot 17054 df-ndx 17066 df-ip 17151 |
This theorem is referenced by: ipndxnbasendx 17213 ipndxnplusgndx 17214 ipndxnmulrndx 17215 slotsdifipndx 17216 ipsstr 17217 phlstr 17227 slotstnscsi 17241 slotsdnscsi 17273 sralemOLD 20639 srascaOLD 20647 sravscaOLD 20649 cchhllemOLD 27836 |
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