Theorem nfunv 6390

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 5675	. 2 ⊢ ¬ Rel V
2		funrel 6374	. 2 ⊢ (Fun V → Rel V)
3	1, 2	mto 199	1 ⊢ ¬ Fun V

Syntax hints:  ¬ wn 3  Vcvv 3496  Rel wrel 5562  Fun wfun 6351

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2795  ax-sep 5205  ax-nul 5212  ax-pr 5332

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2802  df-cleq 2816  df-clel 2895  df-nfc 2965  df-ne 3019  df-v 3498  df-dif 3941  df-un 3943  df-in 3945  df-ss 3954  df-nul 4294  df-if 4470  df-sn 4570  df-pr 4572  df-op 4576  df-opab 5131  df-xp 5563  df-rel 5564  df-fun 6359

This theorem is referenced by: (None)