Theorem nd4

Description: A lemma for proving conditionless ZFC axioms. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Jan-2002) (New usage is discouraged.)

	Ref	Expression
Assertion	nd4	|- ( A. x x = y -> -. A. z y e. x )

Proof

Step	Hyp	Ref	Expression
1		nd3	|- ( A. y y = x -> -. A. z y e. x )
2	1	aecoms	|- ( A. x x = y -> -. A. z y e. x )