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Mirrors > Home > MPE Home > Th. List > basendx | Structured version Visualization version GIF version |
Description: Index value of the base set extractor. (Normally it is preferred to work with (Base‘ndx) rather than the hard-coded 1 in order to make structure theorems portable. This is an example of how to obtain it when needed.) (New usage is discouraged.) (Contributed by Mario Carneiro, 2-Aug-2013.) |
Ref | Expression |
---|---|
basendx | ⊢ (Base‘ndx) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-base 16479 | . 2 ⊢ Base = Slot 1 | |
2 | 1nn 11638 | . 2 ⊢ 1 ∈ ℕ | |
3 | 1, 2 | ndxarg 16498 | 1 ⊢ (Base‘ndx) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ‘cfv 6349 1c1 10527 ndxcnx 16470 Basecbs 16473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2793 ax-sep 5195 ax-nul 5202 ax-pow 5258 ax-pr 5321 ax-un 7450 ax-cnex 10582 ax-1cn 10584 ax-addcl 10586 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3or 1080 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2618 df-eu 2650 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ne 3017 df-ral 3143 df-rex 3144 df-reu 3145 df-rab 3147 df-v 3497 df-sbc 3772 df-csb 3883 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-pss 3953 df-nul 4291 df-if 4466 df-pw 4539 df-sn 4560 df-pr 4562 df-tp 4564 df-op 4566 df-uni 4833 df-iun 4914 df-br 5059 df-opab 5121 df-mpt 5139 df-tr 5165 df-id 5454 df-eprel 5459 df-po 5468 df-so 5469 df-fr 5508 df-we 5510 df-xp 5555 df-rel 5556 df-cnv 5557 df-co 5558 df-dm 5559 df-rn 5560 df-res 5561 df-ima 5562 df-pred 6142 df-ord 6188 df-on 6189 df-lim 6190 df-suc 6191 df-iota 6308 df-fun 6351 df-fn 6352 df-f 6353 df-f1 6354 df-fo 6355 df-f1o 6356 df-fv 6357 df-ov 7148 df-om 7569 df-wrecs 7938 df-recs 7999 df-rdg 8037 df-nn 11628 df-ndx 16476 df-slot 16477 df-base 16479 |
This theorem is referenced by: resslem 16547 1strstr 16588 2strstr 16592 2strstr1 16595 grpbasex 16603 grpplusgx 16604 rngstr 16609 lmodstr 16626 topgrpstr 16651 otpsstr 16658 oppcbas 16978 rescbas 17089 rescabs 17093 catstr 17217 odubas 17733 ipostr 17753 mgpress 19181 cnfldfun 20487 thlbas 20770 indistpsx 21548 tuslem 22805 setsmsbas 23014 trkgstr 26158 eengstr 26694 |
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