Theorem 2moex 2034

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 1429	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 1987	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1527	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2013	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1403	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1287   E.wex 1426   E*wmo 1949

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952

This theorem is referenced by:  2rmorex  2821