Theorem rspe 2435

Description: Restricted specialization. (Contributed by NM, 12-Oct-1999.)

Assertion

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

Proof of Theorem rspe

Step	Hyp	Ref	Expression
1		19.8a 1534	. 2 |- ( ( x e. A /\ ph ) -> E. x ( x e. A /\ ph ) )
2		df-rex 2376	. 2 |- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
3	1, 2	sylibr 133	1 |- ( ( x e. A /\ ph ) -> E. x e. A ph )

Syntax hints:   -> wi 4   /\ wa 103   E.wex 1433   e. wcel 1445   E.wrex 2371

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-4 1452

This theorem depends on definitions:  df-bi 116  df-rex 2376

This theorem is referenced by:  rsp2e  2437  ssiun2  3795  tfrlem9  6122  tfrlemibxssdm  6130  tfr1onlembxssdm  6146  tfrcllembxssdm  6159  findcard2  6685  findcard2s  6686  prarloclemup  7151  prmuloc2  7223  ltaddpr  7253  aptiprlemu  7296  cauappcvgprlemopl  7302  cauappcvgprlemopu  7304  cauappcvgprlem2  7316  caucvgprlemopl  7325  caucvgprlemopu  7327  caucvgprlem2  7336  caucvgprprlem2  7366