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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. (Contributed by Mario Carneiro, 2-Aug-2013.) Use of this theorem is discouraged since the particular value 1 for the index is an implementation detail, see section header comment mmtheorems.html#cnx for more information. (New usage is discouraged.) |
Ref | Expression |
---|---|
basendx | ⊢ (Base‘ndx) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-base 17089 | . 2 ⊢ Base = Slot 1 | |
2 | 1nn 12169 | . 2 ⊢ 1 ∈ ℕ | |
3 | 1, 2 | ndxarg 17073 | 1 ⊢ (Base‘ndx) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ‘cfv 6497 1c1 11057 ndxcnx 17070 Basecbs 17088 |
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-pow 5321 ax-pr 5385 ax-un 7673 ax-cnex 11112 ax-1cn 11114 ax-addcl 11116 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3or 1089 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-ne 2941 df-ral 3062 df-rex 3071 df-reu 3353 df-rab 3407 df-v 3446 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-iun 4957 df-br 5107 df-opab 5169 df-mpt 5190 df-tr 5224 df-id 5532 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-we 5591 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-pred 6254 df-ord 6321 df-on 6322 df-lim 6323 df-suc 6324 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-ov 7361 df-om 7804 df-2nd 7923 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 df-nn 12159 df-slot 17059 df-ndx 17071 df-base 17089 |
This theorem is referenced by: basendxnn 17098 1strstr 17103 2strstr 17110 2strstr1OLD 17114 resslemOLD 17128 basendxltplusgndx 17167 grpbasex 17177 grpplusgx 17178 basendxnmulrndx 17181 rngstr 17184 starvndxnbasendx 17190 scandxnbasendx 17202 vscandxnbasendx 17207 lmodstr 17211 ipndxnbasendx 17218 basendxlttsetndx 17241 topgrpstr 17247 basendxltplendx 17255 otpsstr 17262 basendxnocndx 17269 basendxltdsndx 17274 basendxltunifndx 17284 slotsbhcdif 17301 oppcbasOLD 17605 rescbasOLD 17718 rescabsOLD 17724 catstr 17850 odubasOLD 18186 ipostr 18423 mgpressOLD 19917 cnfldfunALTOLD 20826 thlbasOLD 21117 indistpsx 22376 tuslemOLD 23635 setsmsbasOLD 23845 slotsinbpsd 27425 slotslnbpsd 27426 trkgstr 27428 eengstr 27971 basendxltedgfndx 27986 |
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