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Theorem basendx 11940
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.)
Assertion
Ref Expression
basendx (Base‘ndx) = 1

Proof of Theorem basendx
StepHypRef Expression
1 df-base 11892 . 2 Base = Slot 1
2 1nn 8699 . 2 1 ∈ ℕ
31, 2ndxarg 11909 1 (Base‘ndx) = 1
Colors of variables: wff set class
Syntax hints:   = wceq 1316  cfv 5093  1c1 7589  ndxcnx 11883  Basecbs 11886
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-13 1476  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-pow 4068  ax-pr 4101  ax-un 4325  ax-cnex 7679  ax-resscn 7680  ax-1re 7682  ax-addrcl 7685
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-eu 1980  df-mo 1981  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-sbc 2883  df-un 3045  df-in 3047  df-ss 3054  df-pw 3482  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-int 3742  df-br 3900  df-opab 3960  df-mpt 3961  df-id 4185  df-xp 4515  df-rel 4516  df-cnv 4517  df-co 4518  df-dm 4519  df-rn 4520  df-res 4521  df-iota 5058  df-fun 5095  df-fv 5101  df-inn 8689  df-ndx 11889  df-slot 11890  df-base 11892
This theorem is referenced by:  1strstrg  11984  2strstrg  11986  2strbasg  11987  2stropg  11988  2strstr1g  11989  rngstrg  12001  lmodstrd  12019  topgrpstrd  12037  setsmsbasg  12575
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