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	$$⊢\forall xx=y\to \neg \forall zy\in x$$

Proof

Step	Hyp	Ref	Expression
1		nd3	$$⊢\forall yy=x\to \neg \forall zy\in x$$
2	1	aecoms	$$⊢\forall xx=y\to \neg \forall zy\in x$$