Theorem nfunv 6572

Description: The universal class is not a function. (Contributed by Raph Levien, 27-Jan-2004.)

Assertion

Ref	Expression
nfunv	⊢ ¬ Fun V

Proof of Theorem nfunv

Step	Hyp	Ref	Expression
1		nrelv 5791	. 2 ⊢ ¬ Rel V
2		funrel 6556	. 2 ⊢ (Fun V → Rel V)
3	1, 2	mto 196	1 ⊢ ¬ Fun V

Syntax hints:  ¬ wn 3  Vcvv 3466  Rel wrel 5672  Fun wfun 6528

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-opab 5202  df-xp 5673  df-rel 5674  df-fun 6536

This theorem is referenced by: (None)