Theorem ra4e 1695

Description: Restricted specialization.

Assertion

Ref	Expression
ra4e	|- ((x e. A /\ ph) -> E.x e. A ph)

Proof of Theorem ra4e

Step	Hyp	Ref	Expression
1		19.8a 1029	. 2 |- ((x e. A /\ ph) -> E.x(x e. A /\ ph))
2		df-rex 1650	. 2 |- (E.x e. A ph <-> E.x(x e. A /\ ph))
3	1, 2	sylibr 200	1 |- ((x e. A /\ ph) -> E.x e. A ph)

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

This theorem is referenced by:  uniiunlem 2132  ssiun2 2593  onfr 2986  tfrlem9 3919  oarec 4196  scott0 4717  infxpidmlem7 7558  infxpidmlem8 7559  cncnplem2 7775  atom1d 10280

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

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

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