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Theorem basendxnn 12497
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 )  e.  NN

Proof of Theorem basendxnn
StepHypRef Expression
1 df-base 12448 . . 3  |-  Base  = Slot  1
2 1nn 8916 . . 3  |-  1  e.  NN
31, 2ndxarg 12465 . 2  |-  ( Base `  ndx )  =  1
43, 2eqeltri 2250 1  |-  ( Base `  ndx )  e.  NN
Colors of variables: wff set class
Syntax hints:    e. wcel 2148   ` cfv 5212   1c1 7800   NNcn 8905   ndxcnx 12439   Basecbs 12442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-sep 4118  ax-pow 4171  ax-pr 4206  ax-un 4430  ax-cnex 7890  ax-resscn 7891  ax-1re 7893  ax-addrcl 7896
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-v 2739  df-sbc 2963  df-un 3133  df-in 3135  df-ss 3142  df-pw 3576  df-sn 3597  df-pr 3598  df-op 3600  df-uni 3808  df-int 3843  df-br 4001  df-opab 4062  df-mpt 4063  df-id 4290  df-xp 4629  df-rel 4630  df-cnv 4631  df-co 4632  df-dm 4633  df-rn 4634  df-res 4635  df-iota 5174  df-fun 5214  df-fv 5220  df-inn 8906  df-ndx 12445  df-slot 12446  df-base 12448
This theorem is referenced by:  baseslid  12498  ressvalsets  12503  ressex  12504  resseqnbasd  12511  ressressg  12513  1strbas  12552  2strbasg  12554  2stropg  12555  2strbas1g  12557  rngbaseg  12570  srngbased  12577  lmodbased  12591  ipsbased  12599  tsetndxnbasendx  12610  topgrpbasd  12616  dsndxnbasendx  12627  ring1  13059
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