Theorem ra4e 1687

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 1025	. 2 |- ((x e. A /\ ph) -> E.x(x e. A /\ ph))
2		df-rex 1642	. 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 955  E.wex 977  E.wrex 1638

This theorem is referenced by:  uniiunlem 2122  ssiun2 2583  onfr 2976  tfrlem9 3904  oarec 4180  scott0 4689  infxpidmlem7 7501  infxpidmlem8 7502  cncnplem2 7714  atom1d 10188

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 970

This theorem depends on definitions:  df-bi 147  df-ex 978  df-rex 1642

Copyright terms: Public domain