Theorem reurex 2683

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 2682	. 2 |- ( E! x e. A ph <-> ( E. x e. A ph /\ E* x e. A ph ) )
2	1	simplbi 272	1 |- ( E! x e. A ph -> E. x e. A ph )

Syntax hints:   -> wi 4   E.wrex 2449   E!wreu 2450   E*wrmo 2451

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-nf 1454  df-sb 1756  df-eu 2022  df-mo 2023  df-rex 2454  df-reu 2455  df-rmo 2456

This theorem is referenced by:  reu3  2920  prsrriota  7750  elrealeu  7791  modprm0  12208  ivthinc  13415