Theorem nfunv 6533

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 5757	. 2 ⊢ ¬ Rel V
2		funrel 6517	. 2 ⊢ (Fun V → Rel V)
3	1, 2	mto 197	1 ⊢ ¬ Fun V

Syntax hints:  ¬ wn 3  Vcvv 3442  Rel wrel 5637  Fun wfun 6494

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5243  ax-nul 5253  ax-pr 5379

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-in 3910  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-opab 5163  df-xp 5638  df-rel 5639  df-fun 6502

This theorem is referenced by: (None)