Theorem 2moex 2100

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 1483	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2053	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1578	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2079	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1457	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1341   E.wex 1480   E*wmo 2015

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-eu 2017  df-mo 2018

This theorem is referenced by:  2rmorex  2932