Theorem 2moex 1986

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 1384	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 1939	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1482	. . 3 |- ( ph -> E. y ph )
4	3	moimi 1965	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1358	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1241   E.wex 1381   E*wmo 1901

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904

This theorem is referenced by:  2rmorex  2745