Theorem reurex 1337

Description: Restricted unique existence implies restricted existence.

Assertion

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

Proof of Theorem reurex

Step	Hyp	Ref	Expression
1		euex 1021	. 2 |- (E!x(x e. A /\ ph) -> E.x(x e. A /\ ph))
2		df-reu 1207	. 2 |- (E!x e. A ph <-> E!x(x e. A /\ ph))
3		df-rex 1206	. 2 |- (E.x e. A ph <-> E.x(x e. A /\ ph))
4	1, 2, 3	3imtr4 192	1 |- (E!x e. A ph -> E.x e. A ph)

Syntax hints:   -> wi 2   /\ wa 196  E.wex 678  E!weu 1007   e. wcel 1092  E.wrex 1202  E!wreu 1203

This theorem is referenced by:  reuxfr 1580  reuuni4 1959  oawordex 3159  qbtwnre 4650  hlimreu 5145

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-rex 1206  df-reu 1207

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