Theorem 2eu2ex 2546

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

Assertion

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

Proof of Theorem 2eu2ex

Step	Hyp	Ref	Expression
1		euex 2494	. 2 |- ( E! x E! y ph -> E. x E! y ph )
2		euex 2494	. . 3 |- ( E! y ph -> E. y ph )
3	2	eximi 1762	. 2 |- ( E. x E! y ph -> E. x E. y ph )
4	1, 3	syl 17	1 |- ( E! x E! y ph -> E. x E. y ph )

Syntax hints:   -> wi 4   E.wex 1704   E!weu 2470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-eu 2474

This theorem is referenced by:  2eu1  2553