Theorem bj-cleljusti

Description: One direction of cleljust , requiring only ax-1 -- ax-5 and ax8v1 . (Contributed by BJ, 31-Dec-2020) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-cleljusti	|- ( E. z ( z = x /\ z e. y ) -> x e. y )

Proof

Step	Hyp	Ref	Expression
1		ax8v1	|- ( z = x -> ( z e. y -> x e. y ) )
2	1	imp	|- ( ( z = x /\ z e. y ) -> x e. y )
3	2	exlimiv	|- ( E. z ( z = x /\ z e. y ) -> x e. y )