Theorem nfunv 6515

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 5743	. 2 ⊢ ¬ Rel V
2		funrel 6499	. 2 ⊢ (Fun V → Rel V)
3	1, 2	mto 197	1 ⊢ ¬ Fun V

Syntax hints:  ¬ wn 3  Vcvv 3436  Rel wrel 5624  Fun wfun 6476

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-sep 5235  ax-nul 5245  ax-pr 5371

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ne 2926  df-v 3438  df-dif 3906  df-un 3908  df-ss 3920  df-nul 4285  df-if 4477  df-sn 4578  df-pr 4580  df-op 4584  df-opab 5155  df-xp 5625  df-rel 5626  df-fun 6484

This theorem is referenced by: (None)