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Theorem baseval 12533
Description: 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 NM, 4-Sep-2011.)
Hypothesis
Ref Expression
baseval.k  |-  K  e. 
_V
Assertion
Ref Expression
baseval  |-  ( Base `  K )  =  ( K `  1 )

Proof of Theorem baseval
StepHypRef Expression
1 baseval.k . 2  |-  K  e. 
_V
2 df-base 12486 . 2  |-  Base  = Slot  1
3 1nn 8948 . 2  |-  1  e.  NN
41, 2, 3strnfvn 12501 1  |-  ( Base `  K )  =  ( K `  1 )
Colors of variables: wff set class
Syntax hints:    = wceq 1364    e. wcel 2160   _Vcvv 2752   ` cfv 5231   1c1 7830   Basecbs 12480
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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-13 2162  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4189  ax-pr 4224  ax-un 4448  ax-1re 7923
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2754  df-sbc 2978  df-un 3148  df-in 3150  df-ss 3157  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-int 3860  df-br 4019  df-opab 4080  df-mpt 4081  df-id 4308  df-xp 4647  df-rel 4648  df-cnv 4649  df-co 4650  df-dm 4651  df-rn 4652  df-iota 5193  df-fun 5233  df-fv 5239  df-inn 8938  df-slot 12484  df-base 12486
This theorem is referenced by: (None)
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