Theorem rexlimivw 2658

Description: Weaker version of rexlimiv 2656. (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 2656	1 |- ( E. x e. A ph -> ps )

Syntax hints:   -> wi 4   e. wcel 2205   E.wrex 2523

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-i5r 1584

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-ral 2527  df-rex 2528

This theorem is referenced by:  r19.29vva  2690  eliun  3997  reusv3i  4582  elrnmptg  5011  fun11iun  5637  fmpt  5829  fliftfun  5971  elrnmpo  6169  releldm2  6381  tfrlem4  6546  iinerm  6843  elixpsn  6972  isfi  7002  cardcl  7479  cardval3ex  7483  ltbtwnnqq  7732  recexprlemlol  7943  recexprlemupu  7945  suplocsr  8126  restsspw  13479  rhmdvdsr  14337  ssnei  15033  tgcnp  15091  xmetunirn  15240  metss  15376  metrest  15388  clwwlknun  16453