nfunv - Metamath Proof Explorer

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

Theorem nfunv 6589

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 5804	. 2 ⊢ ¬ Rel V
2		funrel 6573	. 2 ⊢ (Fun V → Rel V)
3	1, 2	mto 196	1 ⊢ ¬ Fun V

Colors of variables: wff setvar class

Syntax hints: ¬ wn 3 Vcvv 3471 Rel wrel 5685 Fun wfun 6545

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 2698 ax-sep 5301 ax-nul 5308 ax-pr 5431

This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2705 df-cleq 2719 df-clel 2805 df-ne 2937 df-v 3473 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4325 df-if 4531 df-sn 4631 df-pr 4633 df-op 4637 df-opab 5213 df-xp 5686 df-rel 5687 df-fun 6553

This theorem is referenced by: (None)

	
		OSZAR »