Theorem 2moex 2086

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 1472	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2039	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1570	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2065	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1446	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1330   E.wex 1469   E*wmo 2001

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004

This theorem is referenced by:  2rmorex  2894