Theorem baseval 17394

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 17393	. 2 ⊢ Base = Slot 1
3	1, 2	strfvn 17369	1 ⊢ (Base‘𝐾) = (𝐾‘1)

This proof depends on syntax axioms:   = wceq 1569   ∈ wcel 2144  Vcvv 3450  ‘cfv 6538  1c1 11204  Basecbs 17392

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-10 2177  ax-11 2193  ax-12 2212  ax-ext 2732  ax-sep 5248  ax-nul 5259  ax-pr 5390

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-nf 1816  df-sb 2099  df-mo 2564  df-eu 2594  df-clab 2739  df-cleq 2752  df-clel 2835  df-nfc 2909  df-ne 2956  df-ral 3077  df-rex 3087  df-rab 3413  df-v 3452  df-ss 3896  df-dif 4047  df-in 4091  df-un 4151  df-nul 4279  df-if 4482  df-sn 4585  df-pr 4587  df-op 4835  df-uni 4867  df-br 5103  df-opab 5167  df-mpt 5186  df-id 5545  df-xp 5656  df-rel 5657  df-cnv 5658  df-co 5659  df-dm 5660  df-iota 6494  df-fun 6540  df-fv 6546  df-slot 17365  df-base 17393

This theorem is used by: (None)