Theorem reurex 1924

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 1392	. 2 |- (E!x(x e. A /\ ph) -> E.x(x e. A /\ ph))
2		df-reu 1648	. 2 |- (E!x e. A ph <-> E!x(x e. A /\ ph))
3		df-rex 1647	. 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 956  E.wex 978  E!weu 1378  E.wrex 1643  E!wreu 1644

This theorem is referenced by:  reu6 1928  reuuni4 2882  reuxfr 2899  oawordex 4181  qbtwnre 6224  hlimreu 9049  cnlnadjt 9950  cdj3lem2b 10298

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-11 965  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-eu 1380  df-rex 1647  df-reu 1648

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