Theorem rexlimivw 2590

Description: Weaker version of rexlimiv 2588. (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 2588	1 |- ( E. x e. A ph -> ps )

Syntax hints:   -> wi 4   e. wcel 2148   E.wrex 2456

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-i5r 1535

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-ral 2460  df-rex 2461

This theorem is referenced by:  r19.29vva  2622  eliun  3892  reusv3i  4461  elrnmptg  4881  fun11iun  5484  fmpt  5668  fliftfun  5799  elrnmpo  5990  releldm2  6188  tfrlem4  6316  iinerm  6609  elixpsn  6737  isfi  6763  cardcl  7182  cardval3ex  7186  ltbtwnnqq  7416  recexprlemlol  7627  recexprlemupu  7629  suplocsr  7810  restsspw  12703  ssnei  13736  tgcnp  13794  xmetunirn  13943  metss  14079  metrest  14091