Theorem 2moex 2166

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 1544	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2118	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1639	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2145	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1518	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1396   E.wex 1541   E*wmo 2080

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-eu 2082  df-mo 2083

This theorem is referenced by:  2rmorex  3013