Theorem 2moex 2131

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 1509	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2084	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1604	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2110	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1483	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1362   E.wex 1506   E*wmo 2046

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-eu 2048  df-mo 2049

This theorem is referenced by:  2rmorex  2970