Theorem 2moex 2128

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 1506	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2081	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1601	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2107	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1480	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1362   E.wex 1503   E*wmo 2043

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2045  df-mo 2046

This theorem is referenced by:  2rmorex  2966