Theorem rexex 1242

Description: Restricted existence implies existence.

Assertion

Ref	Expression
rexex	|- (E.x e. A ph -> E.xph)

Proof of Theorem rexex

Step	Hyp	Ref	Expression
1		df-rex 1206	. 2 |- (E.x e. A ph <-> E.x(x e. A /\ ph))
2		pm3.27 260	. . 3 |- ((x e. A /\ ph) -> ph)
3	2	19.22i 723	. 2 |- (E.x(x e. A /\ ph) -> E.xph)
4	1, 3	sylbi 174	1 |- (E.x e. A ph -> E.xph)

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

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-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-rex 1206

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