Theorem ra4e 1244

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 712	. 2 |- ((x e. A /\ ph) -> E.x(x e. A /\ ph))
2		df-rex 1206	. 2 |- (E.x e. A ph <-> E.x(x e. A /\ ph))
3	1, 2	sylibr 175	1 |- ((x e. A /\ ph) -> E.x e. A ph)

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

This theorem is referenced by:  ssiun2 2019  onfr 2237  tfrlem8 2956  tfrlem9 2957  scott0 3542  infxpidmlem7 4939  infxpidmlem8 4940  atom1d 5750

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673

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

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