Theorem reurex 2581

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 2580	. 2 |- ( E! x e. A ph <-> ( E. x e. A ph /\ E* x e. A ph ) )
2	1	simplbi 269	1 |- ( E! x e. A ph -> E. x e. A ph )

Syntax hints:   -> wi 4   E.wrex 2361   E!wreu 2362   E*wrmo 2363

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474

This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-eu 1952  df-mo 1953  df-rex 2366  df-reu 2367  df-rmo 2368

This theorem is referenced by:  reu3  2806  prsrriota  7394  elrealeu  7428