Theorem 2eu2ex

Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001)

	Ref	Expression
Assertion	2eu2ex	|- ( E! x E! y ph -> E. x E. y ph )

Proof

Step	Hyp	Ref	Expression
1		euex	|- ( E! x E! y ph -> E. x E! y ph )
2		euex	|- ( E! y ph -> E. y ph )
3	2	eximi	|- ( E. x E! y ph -> E. x E. y ph )
4	1 3	syl	|- ( E! x E! y ph -> E. x E. y ph )