Theorem rexex 1693

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 1650	. 2 |- (E.x e. A ph <-> E.x(x e. A /\ ph))
2		pm3.27 323	. . 3 |- ((x e. A /\ ph) -> ph)
3	2	19.22i 1040	. 2 |- (E.x(x e. A /\ ph) -> E.xph)
4	1, 3	sylbi 199	1 |- (E.x e. A ph -> E.xph)

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

This theorem is referenced by:  reu6 1932  dffo5 3821  ivthlem6 7286  ivthlem7 7287

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-rex 1650

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