Theorem 2moex 2139

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 1517	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2092	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1612	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2118	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1491	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1370   E.wex 1514   E*wmo 2054

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-eu 2056  df-mo 2057

This theorem is referenced by:  2rmorex  2978