MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  baseval Structured version   Unicode version

Theorem baseval 13502
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 13466 . 2  |-  Base  = Slot  1
31, 2strfvn 13478 1  |-  ( Base `  K )  =  ( K `  1 )
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725   _Vcvv 2948   ` cfv 5446   1c1 8983   Basecbs 13461
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-slot 13465  df-base 13466
  Copyright terms: Public domain W3C validator