MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfunv Structured version   Visualization version   GIF version

Theorem nfunv 6223
Description: The universe is not a function. (Contributed by Raph Levien, 27-Jan-2004.)
Assertion
Ref Expression
nfunv ¬ Fun V

Proof of Theorem nfunv
StepHypRef Expression
1 nrelv 5524 . 2 ¬ Rel V
2 funrel 6207 . 2 (Fun V → Rel V)
31, 2mto 189 1 ¬ Fun V
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  Vcvv 3415  Rel wrel 5413  Fun wfun 6184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2750  ax-sep 5061  ax-nul 5068  ax-pr 5187
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-ne 2968  df-v 3417  df-dif 3834  df-un 3836  df-in 3838  df-ss 3845  df-nul 4181  df-if 4352  df-sn 4443  df-pr 4445  df-op 4449  df-opab 4993  df-xp 5414  df-rel 5415  df-fun 6192
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator