Theorem baseval 17175

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

Step	Hyp	Ref	Expression
1		baseval.k	. 2 ⊢ 𝐾 ∈ V
2		df-base 17174	. 2 ⊢ Base = Slot 1
3	1, 2	strfvn 17148	1 ⊢ (Base‘𝐾) = (𝐾‘1)

Syntax hints:   = wceq 1534   ∈ wcel 2099  Vcvv 3470  ‘cfv 6542  1c1 11133  Basecbs 17173

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-ext 2699  ax-sep 5293  ax-nul 5300  ax-pr 5423

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2530  df-eu 2559  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-ne 2937  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3472  df-dif 3948  df-un 3950  df-in 3952  df-ss 3962  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4904  df-br 5143  df-opab 5205  df-mpt 5226  df-id 5570  df-xp 5678  df-rel 5679  df-cnv 5680  df-co 5681  df-dm 5682  df-iota 6494  df-fun 6544  df-fv 6550  df-slot 17144  df-base 17174

This theorem is referenced by: (None)