Theorem 2moex 2105

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 1488	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2058	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1583	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2084	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1462	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1346   E.wex 1485   E*wmo 2020

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-eu 2022  df-mo 2023

This theorem is referenced by:  2rmorex  2936