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Theorem baseval 15128
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 15086 . 2  |-  Base  = Slot  1
31, 2strfvn 15098 1  |-  ( Base `  K )  =  ( K `  1 )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437    e. wcel 1867   _Vcvv 3078   ` cfv 5592   1c1 9529   Basecbs 15081
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pr 4652
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-sbc 3297  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4214  df-br 4418  df-opab 4476  df-mpt 4477  df-id 4760  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-iota 5556  df-fun 5594  df-fv 5600  df-slot 15085  df-base 15086
This theorem is referenced by: (None)
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