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Theorem basendxnn 12051
Description: The index value of the base set extractor is a positive integer. This property should be ensured for every concrete coding because otherwise it could not be used in an extensible structure (slots must be positive integers). (Contributed by AV, 23-Sep-2020.)
Assertion
Ref Expression
basendxnn (Base‘ndx) ∈ ℕ

Proof of Theorem basendxnn
StepHypRef Expression
1 df-base 12002 . . 3 Base = Slot 1
2 1nn 8754 . . 3 1 ∈ ℕ
31, 2ndxarg 12019 . 2 (Base‘ndx) = 1
43, 2eqeltri 2213 1 (Base‘ndx) ∈ ℕ
Colors of variables: wff set class
Syntax hints:  wcel 1481  cfv 5130  1c1 7644  cn 8743  ndxcnx 11993  Basecbs 11996
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-13 1492  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4053  ax-pow 4105  ax-pr 4138  ax-un 4362  ax-cnex 7734  ax-resscn 7735  ax-1re 7737  ax-addrcl 7740
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-sbc 2913  df-un 3079  df-in 3081  df-ss 3088  df-pw 3516  df-sn 3537  df-pr 3538  df-op 3540  df-uni 3744  df-int 3779  df-br 3937  df-opab 3997  df-mpt 3998  df-id 4222  df-xp 4552  df-rel 4553  df-cnv 4554  df-co 4555  df-dm 4556  df-rn 4557  df-res 4558  df-iota 5095  df-fun 5132  df-fv 5138  df-inn 8744  df-ndx 11999  df-slot 12000  df-base 12002
This theorem is referenced by:  baseslid  12052  ressval2  12056  ressid  12057  1strbas  12095  2strbasg  12097  2stropg  12098  2strbas1g  12100  rngbaseg  12112  srngbased  12119  lmodbased  12130  ipsbased  12138  topgrpbasd  12148
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