Theorem rexlimivw 2644

Description: Weaker version of rexlimiv 2642. (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 2642	1 |- ( E. x e. A ph -> ps )

Syntax hints:   -> wi 4   e. wcel 2200   E.wrex 2509

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-i5r 1581

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-ral 2513  df-rex 2514

This theorem is referenced by:  r19.29vva  2676  eliun  3969  reusv3i  4550  elrnmptg  4976  fun11iun  5593  fmpt  5785  fliftfun  5920  elrnmpo  6118  releldm2  6331  tfrlem4  6459  iinerm  6754  elixpsn  6882  isfi  6912  cardcl  7353  cardval3ex  7357  ltbtwnnqq  7602  recexprlemlol  7813  recexprlemupu  7815  suplocsr  7996  restsspw  13282  rhmdvdsr  14139  ssnei  14825  tgcnp  14883  xmetunirn  15032  metss  15168  metrest  15180