Mathbox for Alexander van der Vekens < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ndmafv Structured version   Unicode version

Theorem ndmafv 27980
 Description: The value of a class outside its domain is the universe, compare with ndmfv 5755. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
ndmafv '''

Proof of Theorem ndmafv
StepHypRef Expression
1 df-dfat 27950 . . . 4 defAt
21simplbi 447 . . 3 defAt
32con3i 129 . 2 defAt
4 afvnfundmuv 27979 . 2 defAt '''
53, 4syl 16 1 '''
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1652   wcel 1725  cvv 2956  csn 3814   cdm 4878   cres 4880   wfun 5448   defAt wdfat 27947  '''cafv 27948 This theorem is referenced by:  afvvdm  27981  afvprc  27984  afvco2  28016  ndmaov  28023  aovprc  28028 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-un 3325  df-if 3740  df-fv 5462  df-dfat 27950  df-afv 27951
 Copyright terms: Public domain W3C validator