Theorem reurex 1928

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 1394	. 2 |- (E!x(x e. A /\ ph) -> E.x(x e. A /\ ph))
2		df-reu 1651	. 2 |- (E!x e. A ph <-> E!x(x e. A /\ ph))
3		df-rex 1650	. 2 |- (E.x e. A ph <-> E.x(x e. A /\ ph))
4	1, 2, 3	3imtr4 219	1 |- (E!x e. A ph -> E.x e. A ph)

Syntax hints:   -> wi 3   /\ wa 223   e. wcel 958  E.wex 980  E!weu 1380  E.wrex 1646  E!wreu 1647

This theorem is referenced by:  reu6 1932  reuuni4 2887  reuxfr 2904  oawordex 4191  qbtwnre 6278  hlimreu 9110  cnlnadjt 10012  cdj3lem2b 10364

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-rex 1650  df-reu 1651

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