Theorem reurex 2750

Description: Restricted unique existence implies restricted existence. (Contributed by NM, 19-Aug-1999.)

Assertion

Ref	Expression
reurex	|- ( E! x e. A ph -> E. x e. A ph )

Proof of Theorem reurex

Step	Hyp	Ref	Expression
1		reu5 2749	. 2 |- ( E! x e. A ph <-> ( E. x e. A ph /\ E* x e. A ph ) )
2	1	simplbi 274	1 |- ( E! x e. A ph -> E. x e. A ph )

Syntax hints:   -> wi 4   E.wrex 2509   E!wreu 2510   E*wrmo 2511

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081  df-rex 2514  df-reu 2515  df-rmo 2516

This theorem is referenced by:  reu3  2993  prsrriota  7971  elrealeu  8012  modprm0  12772  issrgid  13939  isringid  13983  ivthinc  15311