Theorem ruv

Description: The Russell class is equal to the universe _V . Exercise 5 of TakeutiZaring p. 22. (Contributed by Alan Sare, 4-Oct-2008)

	Ref	Expression
Assertion	ruv	|- { x | x e/ x } = _V

Proof

Step	Hyp	Ref	Expression
1		df-v	|- _V = { x | x = x }
2		equid	|- x = x
3		elirrv	|- -. x e. x
4	3	nelir	|- x e/ x
5	2 4	2th	|- ( x = x <-> x e/ x )
6	5	abbii	|- { x | x = x } = { x | x e/ x }
7	1 6	eqtr2i	|- { x | x e/ x } = _V