Theorem rexlimivw 2619

Description: Weaker version of rexlimiv 2617. (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 2617	1 |- ( E. x e. A ph -> ps )

Syntax hints:   -> wi 4   e. wcel 2176   E.wrex 2485

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-ral 2489  df-rex 2490

This theorem is referenced by:  r19.29vva  2651  eliun  3931  reusv3i  4507  elrnmptg  4931  fun11iun  5545  fmpt  5732  fliftfun  5867  elrnmpo  6061  releldm2  6273  tfrlem4  6401  iinerm  6696  elixpsn  6824  isfi  6854  cardcl  7290  cardval3ex  7294  ltbtwnnqq  7530  recexprlemlol  7741  recexprlemupu  7743  suplocsr  7924  restsspw  13114  rhmdvdsr  13970  ssnei  14656  tgcnp  14714  xmetunirn  14863  metss  14999  metrest  15011