Theorem 2moex 2140

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 1518	. . 3 |- ( E. y ph -> A. y E. y ph )
2	1	hbmo 2093	. 2 |- ( E* x E. y ph -> A. y E* x E. y ph )
3		19.8a 1613	. . 3 |- ( ph -> E. y ph )
4	3	moimi 2119	. 2 |- ( E* x E. y ph -> E* x ph )
5	2, 4	alrimih 1492	1 |- ( E* x E. y ph -> A. y E* x ph )

Syntax hints:   -> wi 4   A.wal 1371   E.wex 1515   E*wmo 2055

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-eu 2057  df-mo 2058

This theorem is referenced by:  2rmorex  2979