Theorem rexlimivw 2485

Description: Weaker version of rexlimiv 2483. (Contributed by FL, 19-Sep-2011.)

Hypothesis

Ref	Expression
rexlimivw.1	|- ( ph -> ps )

Assertion

Ref	Expression
rexlimivw	|- ( E. x e. A ph -> ps )

Distinct variable group:   ps, x

Allowed substitution hints:   ph( x)   A( x)

Proof of Theorem rexlimivw

Step	Hyp	Ref	Expression
1		rexlimivw.1	. . 3 |- ( ph -> ps )
2	1	a1i 9	. 2 |- ( x e. A -> ( ph -> ps ) )
3	2	rexlimiv 2483	1 |- ( E. x e. A ph -> ps )

Syntax hints:   -> wi 4   e. wcel 1438   E.wrex 2360

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-i5r 1473

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-ral 2364  df-rex 2365

This theorem is referenced by:  r19.29vva  2513  eliun  3734  reusv3i  4281  elrnmptg  4687  fun11iun  5274  fmpt  5449  fliftfun  5575  elrnmpt2  5758  releldm2  5955  tfrlem4  6078  iinerm  6362  isfi  6476  cardcl  6807  cardval3ex  6811  ltbtwnnqq  6972  recexprlemlol  7183  recexprlemupu  7185