Theorem 2moex 2164

Description: Double quantification with "at most one". (Contributed by NM, 3-Dec-2001.)

Assertion

Ref	Expression
2moex	|- ( E* x E. y ph -> A. y E* x ph )

Proof of Theorem 2moex

Step	Hyp	Ref	Expression
1		hbe1 1541	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2116	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1636	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2143	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1515	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1393   E.wex 1538   E*wmo 2078

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-tru 1398  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081

This theorem is referenced by:  2rmorex  3009