Theorem 2moex 2027

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 1424	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 1980	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1522	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2006	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1398	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1282   E.wex 1421   E*wmo 1942

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-eu 1944  df-mo 1945

This theorem is referenced by:  2rmorex  2796