Theorem zfcndreg

Description: Axiom of Regularity ax-reg , reproved from conditionless ZFC axioms. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 15-Aug-2003) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	zfcndreg	|- ( E. y y e. x -> E. y ( y e. x /\ A. z ( z e. y -> -. z e. x ) ) )

Proof

Step	Hyp	Ref	Expression
1		nfe1	|- F/ y E. y ( y e. x /\ A. z ( z e. y -> -. z e. x ) )
2		axregnd	|- ( y e. x -> E. y ( y e. x /\ A. z ( z e. y -> -. z e. x ) ) )
3	1 2	exlimi	|- ( E. y y e. x -> E. y ( y e. x /\ A. z ( z e. y -> -. z e. x ) ) )