Theorem rexlimivw 2610

Description: Weaker version of rexlimiv 2608. (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 2608	1 |- ( E. x e. A ph -> ps )

Syntax hints:   -> wi 4   e. wcel 2167   E.wrex 2476

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-ral 2480  df-rex 2481

This theorem is referenced by:  r19.29vva  2642  eliun  3920  reusv3i  4494  elrnmptg  4918  fun11iun  5525  fmpt  5712  fliftfun  5843  elrnmpo  6036  releldm2  6243  tfrlem4  6371  iinerm  6666  elixpsn  6794  isfi  6820  cardcl  7248  cardval3ex  7252  ltbtwnnqq  7482  recexprlemlol  7693  recexprlemupu  7695  suplocsr  7876  restsspw  12920  rhmdvdsr  13731  ssnei  14387  tgcnp  14445  xmetunirn  14594  metss  14730  metrest  14742