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Theorem baseval 17187
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 ∈ V
Assertion
Ref Expression
baseval (Base‘𝐾) = (𝐾‘1)

Proof of Theorem baseval
StepHypRef Expression
1 baseval.k . 2 𝐾 ∈ V
2 df-base 17186 . 2 Base = Slot 1
31, 2strfvn 17160 1 (Base‘𝐾) = (𝐾‘1)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  Vcvv 3471  cfv 6551  1c1 11145  Basecbs 17185
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2698  ax-sep 5301  ax-nul 5308  ax-pr 5431
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2529  df-eu 2558  df-clab 2705  df-cleq 2719  df-clel 2805  df-nfc 2880  df-ne 2937  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4911  df-br 5151  df-opab 5213  df-mpt 5234  df-id 5578  df-xp 5686  df-rel 5687  df-cnv 5688  df-co 5689  df-dm 5690  df-iota 6503  df-fun 6553  df-fv 6559  df-slot 17156  df-base 17186
This theorem is referenced by: (None)
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