Theorem 2eu2ex 2167

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 2107	. 2 |- ( E! x E! y ph -> E. x E! y ph )
2		euex 2107	. . 3 |- ( E! y ph -> E. y ph )
3	2	eximi 1646	. 2 |- ( E. x E! y ph -> E. x E. y ph )
4	1, 3	syl 14	1 |- ( E! x E! y ph -> E. x E. y ph )

Syntax hints:   -> wi 4   E.wex 1538   E!weu 2077

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-eu 2080

This theorem is referenced by: (None)